AFLOW Prototype: A5B40CD12_cP116_224_bd_e3k_a_k-001
This structure originally had the label A5B40CD12_cP116_224_cd_e3k_a_k. Calls to that address will be redirected here.
If you are using this page, please cite:
D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)
Links to this page
https://aflow.org/p/E8XB
or
https://aflow.org/p/A5B40CD12_cP116_224_bd_e3k_a_k-001
or
PDF Version
Prototype | (H$_{2}$O)$_{5}$O$_{40}$PW$_{12}$ |
AFLOW prototype label | A5B40CD12_cP116_224_bd_e3k_a_k-001 |
Strukturbericht designation | $H4_{16}$ |
Mineral name | 12-phosphotungstic acid |
ICSD | 31897 |
Pearson symbol | cP116 |
Space group number | 224 |
Space group symbol | $Pn\overline{3}m$ |
AFLOW prototype command |
aflow --proto=A5B40CD12_cP116_224_bd_e3k_a_k-001
--params=$a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}$ |
Basis vectors
Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
---|---|---|---|---|---|---|
$\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (2a) | P I |
$\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (2a) | P I |
$\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (4b) | H I |
$\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4b) | H I |
$\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | H I |
$\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | H I |
$\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{9}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{10}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{11}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{12}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6d) | H II |
$\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{14}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{15}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{16}}$ | = | $x_{4} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{17}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{19}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{20}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8e) | O I |
$\mathbf{B_{21}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{22}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{23}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{24}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{25}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{26}}$ | = | $z_{5} \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{27}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{28}}$ | = | $- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{29}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{30}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{31}}$ | = | $x_{5} \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{32}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{33}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{34}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{35}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{36}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{37}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{38}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{39}}$ | = | $- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{40}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{41}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{42}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{43}}$ | = | $- z_{5} \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{44}}$ | = | $- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (24k) | O II |
$\mathbf{B_{45}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{46}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{47}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{48}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{49}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{50}}$ | = | $z_{6} \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{51}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{52}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{53}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{54}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{55}}$ | = | $x_{6} \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{56}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{57}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{58}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{59}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{60}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{61}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{62}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{63}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{64}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{65}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{66}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{67}}$ | = | $- z_{6} \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{68}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (24k) | O III |
$\mathbf{B_{69}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{70}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{71}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{72}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{73}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{74}}$ | = | $z_{7} \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{75}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{76}}$ | = | $- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{77}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{78}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{79}}$ | = | $x_{7} \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{80}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{81}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{82}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{83}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{84}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{85}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{86}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{87}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{88}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{89}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{90}}$ | = | $\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{91}}$ | = | $- z_{7} \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{92}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (24k) | O IV |
$\mathbf{B_{93}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{94}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{95}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{96}}$ | = | $x_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{97}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{98}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{99}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{100}}$ | = | $- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{101}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{102}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{8} \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{103}}$ | = | $x_{8} \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{104}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{105}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{106}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a z_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{107}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{108}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{109}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{110}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{111}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{112}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a z_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{113}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{114}}$ | = | $\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{115}}$ | = | $- z_{8} \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24k) | W I |
$\mathbf{B_{116}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $- a z_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (24k) | W I |