Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B3C6_cP264_205_2d_ab2c2d_6d-001

This structure originally had the label A2B3C6_cP264_205_2d_ab2c2d_6d. Calls to that address will be redirected here.

If you are using this page, please cite:
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)

Links to this page

https://aflow.org/p/Q2JD
or https://aflow.org/p/A2B3C6_cP264_205_2d_ab2c2d_6d-001
or PDF Version

Ca$_{3}$Al$_{2}$O$_{6}$ Structure: A2B3C6_cP264_205_2d_ab2c2d_6d-001

Picture of Structure; Click for Big Picture
Prototype Al$_{2}$Ca$_{3}$O$_{6}$
AFLOW prototype label A2B3C6_cP264_205_2d_ab2c2d_6d-001
ICSD 1841
Pearson symbol cP264
Space group number 205
Space group symbol $Pa\overline{3}$
AFLOW prototype command aflow --proto=A2B3C6_cP264_205_2d_ab2c2d_6d-001
--params=$a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}$


\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (4a) Ca I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{3}}$ = $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ (4a) Ca I
$\mathbf{B_{4}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ (4a) Ca I
$\mathbf{B_{5}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ (4b) Ca II
$\mathbf{B_{6}}$ = $\frac{1}{2} \, \mathbf{a}_{2}$ = $\frac{1}{2}a \,\mathbf{\hat{y}}$ (4b) Ca II
$\mathbf{B_{7}}$ = $\frac{1}{2} \, \mathbf{a}_{1}$ = $\frac{1}{2}a \,\mathbf{\hat{x}}$ (4b) Ca II
$\mathbf{B_{8}}$ = $\frac{1}{2} \, \mathbf{a}_{3}$ = $\frac{1}{2}a \,\mathbf{\hat{z}}$ (4b) Ca II
$\mathbf{B_{9}}$ = $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{10}}$ = $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{11}}$ = $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{12}}$ = $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{13}}$ = $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{14}}$ = $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{15}}$ = $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{16}}$ = $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ (8c) Ca III
$\mathbf{B_{17}}$ = $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{18}}$ = $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{19}}$ = $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{20}}$ = $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{21}}$ = $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{22}}$ = $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{23}}$ = $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{24}}$ = $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ (8c) Ca IV
$\mathbf{B_{25}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{26}}$ = $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{27}}$ = $- x_{5} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{28}}$ = $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{29}}$ = $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ = $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{30}}$ = $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ = $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{31}}$ = $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{32}}$ = $- z_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{33}}$ = $y_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{34}}$ = $- y_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{35}}$ = $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{36}}$ = $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{37}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{38}}$ = $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{39}}$ = $x_{5} \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{40}}$ = $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{41}}$ = $- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ = $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{42}}$ = $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ = $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{43}}$ = $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{44}}$ = $z_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{45}}$ = $- y_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{46}}$ = $y_{5} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{47}}$ = $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{48}}$ = $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al I
$\mathbf{B_{49}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{50}}$ = $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{51}}$ = $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{52}}$ = $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{53}}$ = $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ = $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{54}}$ = $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ = $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{55}}$ = $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{56}}$ = $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{57}}$ = $y_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{58}}$ = $- y_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{59}}$ = $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{60}}$ = $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{61}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{62}}$ = $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{63}}$ = $x_{6} \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{64}}$ = $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{65}}$ = $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ = $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{66}}$ = $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ = $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{67}}$ = $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{68}}$ = $z_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{69}}$ = $- y_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{70}}$ = $y_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{71}}$ = $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{72}}$ = $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Al II
$\mathbf{B_{73}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{74}}$ = $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{75}}$ = $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{76}}$ = $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{77}}$ = $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ = $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{78}}$ = $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ = $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{79}}$ = $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{80}}$ = $- z_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{81}}$ = $y_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{82}}$ = $- y_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{83}}$ = $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ = $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{84}}$ = $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{85}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{86}}$ = $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{87}}$ = $x_{7} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{88}}$ = $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{89}}$ = $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ = $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{90}}$ = $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ = $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{91}}$ = $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{92}}$ = $z_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{93}}$ = $- y_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{94}}$ = $y_{7} \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{95}}$ = $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ = $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{96}}$ = $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca V
$\mathbf{B_{97}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{98}}$ = $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{99}}$ = $- x_{8} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{100}}$ = $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{101}}$ = $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ = $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{102}}$ = $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ = $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{103}}$ = $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{104}}$ = $- z_{8} \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{105}}$ = $y_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ = $a y_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{106}}$ = $- y_{8} \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{8} \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{107}}$ = $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ = $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{108}}$ = $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{109}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{110}}$ = $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{111}}$ = $x_{8} \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{112}}$ = $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{113}}$ = $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ = $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a y_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{114}}$ = $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ = $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{115}}$ = $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{116}}$ = $z_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{117}}$ = $- y_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ = $- a y_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{118}}$ = $y_{8} \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{8} \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{119}}$ = $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ = $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{120}}$ = $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) Ca VI
$\mathbf{B_{121}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{122}}$ = $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{123}}$ = $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{124}}$ = $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{125}}$ = $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ = $a z_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{126}}$ = $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ = $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{127}}$ = $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{128}}$ = $- z_{9} \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{129}}$ = $y_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ = $a y_{9} \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{130}}$ = $- y_{9} \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{9} \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{131}}$ = $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ = $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{132}}$ = $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{133}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- a z_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{134}}$ = $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{135}}$ = $x_{9} \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{136}}$ = $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{137}}$ = $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ = $- a z_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a y_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{138}}$ = $- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ = $- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{139}}$ = $\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{140}}$ = $z_{9} \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{141}}$ = $- y_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ = $- a y_{9} \,\mathbf{\hat{x}}- a z_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{142}}$ = $y_{9} \, \mathbf{a}_{1}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{9} \,\mathbf{\hat{x}}- a \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{143}}$ = $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ = $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{144}}$ = $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{9} \,\mathbf{\hat{y}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O I
$\mathbf{B_{145}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{146}}$ = $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{147}}$ = $- x_{10} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{148}}$ = $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{149}}$ = $z_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ = $a z_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{150}}$ = $\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ = $a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{151}}$ = $- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{152}}$ = $- z_{10} \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{153}}$ = $y_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ = $a y_{10} \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{154}}$ = $- y_{10} \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{10} \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{155}}$ = $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ = $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{156}}$ = $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{157}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- a z_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{158}}$ = $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{159}}$ = $x_{10} \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{160}}$ = $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{161}}$ = $- z_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- y_{10} \, \mathbf{a}_{3}$ = $- a z_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a y_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{162}}$ = $- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{10} \, \mathbf{a}_{3}$ = $- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{163}}$ = $\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{164}}$ = $z_{10} \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{165}}$ = $- y_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ = $- a y_{10} \,\mathbf{\hat{x}}- a z_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{166}}$ = $y_{10} \, \mathbf{a}_{1}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{10} \,\mathbf{\hat{x}}- a \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{167}}$ = $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ = $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{168}}$ = $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{10} \,\mathbf{\hat{y}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O II
$\mathbf{B_{169}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{170}}$ = $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{171}}$ = $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{172}}$ = $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{173}}$ = $z_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ = $a z_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{174}}$ = $\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ = $a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{175}}$ = $- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{176}}$ = $- z_{11} \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{177}}$ = $y_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ = $a y_{11} \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{178}}$ = $- y_{11} \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{11} \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{179}}$ = $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ = $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{180}}$ = $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{181}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- a z_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{182}}$ = $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{183}}$ = $x_{11} \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{184}}$ = $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{185}}$ = $- z_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- y_{11} \, \mathbf{a}_{3}$ = $- a z_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a y_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{186}}$ = $- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{11} \, \mathbf{a}_{3}$ = $- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{187}}$ = $\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{188}}$ = $z_{11} \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{189}}$ = $- y_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ = $- a y_{11} \,\mathbf{\hat{x}}- a z_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{190}}$ = $y_{11} \, \mathbf{a}_{1}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{11} \,\mathbf{\hat{x}}- a \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{191}}$ = $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ = $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{192}}$ = $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{11} \,\mathbf{\hat{y}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O III
$\mathbf{B_{193}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+a z_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{194}}$ = $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{195}}$ = $- x_{12} \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{196}}$ = $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{197}}$ = $z_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ = $a z_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+a y_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{198}}$ = $\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ = $a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{199}}$ = $- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{200}}$ = $- z_{12} \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{12} \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{201}}$ = $y_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ = $a y_{12} \,\mathbf{\hat{x}}+a z_{12} \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{202}}$ = $- y_{12} \, \mathbf{a}_{1}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{12} \,\mathbf{\hat{x}}+a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{203}}$ = $\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ = $a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{204}}$ = $- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{12} \,\mathbf{\hat{y}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{205}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}- a z_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{206}}$ = $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{207}}$ = $x_{12} \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{208}}$ = $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{209}}$ = $- z_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ = $- a z_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- a y_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{210}}$ = $- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ = $- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{211}}$ = $\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{212}}$ = $z_{12} \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{12} \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{213}}$ = $- y_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ = $- a y_{12} \,\mathbf{\hat{x}}- a z_{12} \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{214}}$ = $y_{12} \, \mathbf{a}_{1}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{12} \,\mathbf{\hat{x}}- a \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{215}}$ = $- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ = $- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{216}}$ = $\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{12} \,\mathbf{\hat{y}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O IV
$\mathbf{B_{217}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+a z_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{218}}$ = $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{219}}$ = $- x_{13} \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{220}}$ = $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ = $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{221}}$ = $z_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ = $a z_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+a y_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{222}}$ = $\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ = $a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{223}}$ = $- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{224}}$ = $- z_{13} \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{13} \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{225}}$ = $y_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ = $a y_{13} \,\mathbf{\hat{x}}+a z_{13} \,\mathbf{\hat{y}}+a x_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{226}}$ = $- y_{13} \, \mathbf{a}_{1}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{13} \,\mathbf{\hat{x}}+a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{227}}$ = $\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ = $a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{228}}$ = $- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{13} \,\mathbf{\hat{y}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{229}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}- a z_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{230}}$ = $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{231}}$ = $x_{13} \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{232}}$ = $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{233}}$ = $- z_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ = $- a z_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- a y_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{234}}$ = $- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ = $- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{235}}$ = $\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{236}}$ = $z_{13} \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{13} \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{237}}$ = $- y_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ = $- a y_{13} \,\mathbf{\hat{x}}- a z_{13} \,\mathbf{\hat{y}}- a x_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{238}}$ = $y_{13} \, \mathbf{a}_{1}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{13} \,\mathbf{\hat{x}}- a \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{239}}$ = $- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ = $- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{13} \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{240}}$ = $\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{13} \,\mathbf{\hat{y}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O V
$\mathbf{B_{241}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+a z_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{242}}$ = $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{243}}$ = $- x_{14} \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{244}}$ = $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ = $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{245}}$ = $z_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ = $a z_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+a y_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{246}}$ = $\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ = $a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a y_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{247}}$ = $- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{248}}$ = $- z_{14} \, \mathbf{a}_{1}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a z_{14} \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{249}}$ = $y_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ = $a y_{14} \,\mathbf{\hat{x}}+a z_{14} \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{250}}$ = $- y_{14} \, \mathbf{a}_{1}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a y_{14} \,\mathbf{\hat{x}}+a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{251}}$ = $\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ = $a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{252}}$ = $- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{14} \,\mathbf{\hat{y}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{253}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}- a z_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{254}}$ = $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{255}}$ = $x_{14} \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{256}}$ = $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{257}}$ = $- z_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ = $- a z_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- a y_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{258}}$ = $- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ = $- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{259}}$ = $\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{260}}$ = $z_{14} \, \mathbf{a}_{1}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a z_{14} \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{261}}$ = $- y_{14} \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ = $- a y_{14} \,\mathbf{\hat{x}}- a z_{14} \,\mathbf{\hat{y}}- a x_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{262}}$ = $y_{14} \, \mathbf{a}_{1}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a y_{14} \,\mathbf{\hat{x}}- a \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{263}}$ = $- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ = $- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{14} \,\mathbf{\hat{z}}$ (24d) O VI
$\mathbf{B_{264}}$ = $\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{14} \,\mathbf{\hat{y}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (24d) O VI

References

  • P. Mondal and J. W. Jeffery, The crystal structure of tricalcium aluminate, Ca$_{3}$Al$_{2}$O$_{6}$, Acta Crystallogr. Sect. B 31, 689–697 (1975), doi:10.1107/S0567740875003639.

Prototype Generator

aflow --proto=A2B3C6_cP264_205_2d_ab2c2d_6d --params=$a,x_{3},x_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14}$

Species:

Running:

Output: