Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A12B36CD12_cF488_210_h_3h_a_fg-001

This structure originally had the label A12B36CD12_cF488_210_h_3h_a_fg. 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/X29X
or https://aflow.org/p/A12B36CD12_cF488_210_h_3h_a_fg-001
or PDF Version

MgB$_{12}$H$_{12}$[H$_{2}$O]$_{12}$ Structure: A12B36CD12_cF488_210_h_3h_a_fg-001

Picture of Structure; Click for Big Picture
Prototype B$_{12}$H$_{36}$MgO$_{12}$
AFLOW prototype label A12B36CD12_cF488_210_h_3h_a_fg-001
ICSD 413594
Pearson symbol cF488
Space group number 210
Space group symbol $F4_132$
AFLOW prototype command aflow --proto=A12B36CD12_cF488_210_h_3h_a_fg-001
--params=$a, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$

Other compounds with this structure

NiB$_{12}$H$_{12}$[H$_{2}$O]$_{12}$


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

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $0$ = $0$ (8a) Mg I
$\mathbf{B_{2}}$ = $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ (8a) Mg I
$\mathbf{B_{3}}$ = $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}$ (48f) O I
$\mathbf{B_{4}}$ = $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}$ (48f) O I
$\mathbf{B_{5}}$ = $x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{y}}$ (48f) O I
$\mathbf{B_{6}}$ = $- x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{y}}$ (48f) O I
$\mathbf{B_{7}}$ = $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{8}}$ = $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{9}}$ = $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{10}}$ = $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{11}}$ = $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{12}}$ = $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{13}}$ = $- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{14}}$ = $\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (48f) O I
$\mathbf{B_{15}}$ = $\frac{1}{8} \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ = $\frac{5}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{16}}$ = $- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{17}}$ = $\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ = $\frac{3}{8}a \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{18}}$ = $\frac{5}{8} \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ = $\frac{5}{8}a \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{19}}$ = $\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{20}}$ = $\frac{5}{8} \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{21}}$ = $\frac{1}{8} \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{22}}$ = $- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{x}}+\frac{5}{8}a \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{23}}$ = $- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{24}}$ = $\frac{1}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{25}}$ = $\frac{5}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{26}}$ = $\left(2 y_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(2 y_{3} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}a \,\mathbf{\hat{z}}$ (48g) O II
$\mathbf{B_{27}}$ = $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{28}}$ = $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{29}}$ = $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{30}}$ = $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{31}}$ = $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{32}}$ = $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{33}}$ = $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{34}}$ = $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ = $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{35}}$ = $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{36}}$ = $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{37}}$ = $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ = $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{38}}$ = $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ = $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{39}}$ = $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{40}}$ = $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{41}}$ = $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{42}}$ = $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{43}}$ = $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{44}}$ = $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{45}}$ = $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{46}}$ = $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{47}}$ = $- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{48}}$ = $\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{49}}$ = $\left(x_{4} + y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{50}}$ = $- \left(x_{4} + y_{4} - z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) B I
$\mathbf{B_{51}}$ = $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{52}}$ = $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{53}}$ = $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{54}}$ = $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{55}}$ = $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{56}}$ = $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{57}}$ = $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{58}}$ = $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ = $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{59}}$ = $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{60}}$ = $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{61}}$ = $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{62}}$ = $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{63}}$ = $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{64}}$ = $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{65}}$ = $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{66}}$ = $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{67}}$ = $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{68}}$ = $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{69}}$ = $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{70}}$ = $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{71}}$ = $- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{72}}$ = $\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{73}}$ = $\left(x_{5} + y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{74}}$ = $- \left(x_{5} + y_{5} - z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H I
$\mathbf{B_{75}}$ = $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{76}}$ = $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+a z_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{77}}$ = $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{78}}$ = $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- a z_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{79}}$ = $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{80}}$ = $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{81}}$ = $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a z_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a y_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{82}}$ = $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ = $- a z_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a y_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{83}}$ = $\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{84}}$ = $\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}+a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{85}}$ = $- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{3}$ = $a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{86}}$ = $\left(x_{6} + y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} + z_{6}\right) \, \mathbf{a}_{3}$ = $- a y_{6} \,\mathbf{\hat{x}}- a z_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{87}}$ = $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{88}}$ = $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{89}}$ = $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{90}}$ = $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{91}}$ = $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{92}}$ = $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{93}}$ = $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{94}}$ = $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{95}}$ = $- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{96}}$ = $\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{97}}$ = $\left(x_{6} + y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{98}}$ = $- \left(x_{6} + y_{6} - z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} - y_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H II
$\mathbf{B_{99}}$ = $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{100}}$ = $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+a z_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{101}}$ = $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{102}}$ = $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- a z_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{103}}$ = $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{104}}$ = $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{105}}$ = $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a z_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a y_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{106}}$ = $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ = $- a z_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a y_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{107}}$ = $\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{108}}$ = $\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}+a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{109}}$ = $- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{3}$ = $a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{110}}$ = $\left(x_{7} + y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} + z_{7}\right) \, \mathbf{a}_{3}$ = $- a y_{7} \,\mathbf{\hat{x}}- a z_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{111}}$ = $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{112}}$ = $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{113}}$ = $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{114}}$ = $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{115}}$ = $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{116}}$ = $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{117}}$ = $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{118}}$ = $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{119}}$ = $- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{120}}$ = $\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{121}}$ = $\left(x_{7} + y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III
$\mathbf{B_{122}}$ = $- \left(x_{7} + y_{7} - z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} - y_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (96h) H III

References

  • I. Tiritiris and T. Schleid, Synthese, Kristallstruktur und thermischer Abbau von Mg(H$_{2}$O)$_{6}$[B$_{12}$H$_{12}$] $\cdot$ 6H$_{2}$O, Zeitschrift für anorganische und allgemeine Chemie 630, 541–546 (2004).

Found in

  • I. Tiritiris and T. Schleid, Synthesis, Crystal Structure, and Thermal Decomposition of Mg(H$_{2}$O)$_{6}$[B$_{12}$H$_{1}$2]$\times$6H$_{2}$O, ChemInform (2004), doi:10.1002/chin.200425008.
  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.

Prototype Generator

aflow --proto=A12B36CD12_cF488_210_h_3h_a_fg --params=$a,x_{2},y_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7}$

Species:

Running:

Output: