α-AlB$_{12}$ Structure: A5B22_tP216_96_5b_2a21b-001
| Prototype | AlB$_{12}$ |
| AFLOW prototype label | A5B22_tP216_96_5b_2a21b-001 |
| ICSD | 1091 |
| Pearson symbol | tP216 |
| Space group number | 96 |
| Space group symbol | $P4_32_12$ |
| AFLOW prototype command |
aflow --proto=A5B22_tP216_96_5b_2a21b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}$ |
- AlB$_{12}$ can also be found as orthorhombic $\gamma$–AlB$_{12}$. Unfortunately we do not have a determination of the atomic positions in that system.
- As the $\gamma$ structure has never been isolated from the $\alpha$ structure, and can be transformed into the $\alpha$ structure but not reconstituted from it, $\alpha$–AlB$_{12}$ is the ground state of the system. (Higashi, 2000)
- According to (Higashi, 1977), there are thirteen aluminum atoms in this cell, distributed statistically among the five sites. This gives a stoichiometry of Al$_{0.88}$B$_{12}$. The sites Al-I, Al-III, and Al-V are extremely close together. The combined site is 98% occupied, and only one site is occupied at any one position, so the occupancy of these sites are approximately 33%. Similarly, pairs of Al-II atoms are rather close together, and each pair of sites contains approximately 98%, giving an occupation of 49% for the A-II site. If there are thirteen aluminum atoms in the unit cell, puts the occupation of the Al-IV site at 14.5%.
- This structure can also be found in the enantiomorphic space group $P4_{1}2_{1}2$ #92. We follow the authors and place it in $P4_{3}2_{1}2$ #96.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}$ | (4a) | B I |
| $\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | B I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}$ | (4a) | B II |
| $\mathbf{B_{6}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | B II |
| $\mathbf{B_{7}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | B II |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | B II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{10}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{12}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{15}}$ | = | $y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{16}}$ | = | $- y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al I |
| $\mathbf{B_{17}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{18}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{19}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{20}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{22}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{23}}$ | = | $y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{24}}$ | = | $- y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al II |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{26}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{27}}$ | = | $- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{28}}$ | = | $\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{29}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{31}}$ | = | $y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{32}}$ | = | $- y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al III |
| $\mathbf{B_{33}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{34}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{35}}$ | = | $- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{36}}$ | = | $\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{37}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{38}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{39}}$ | = | $y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{40}}$ | = | $- y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al IV |
| $\mathbf{B_{41}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{42}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{43}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{44}}$ | = | $\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{45}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{46}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{47}}$ | = | $y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{48}}$ | = | $- y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | Al V |
| $\mathbf{B_{49}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{50}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{51}}$ | = | $- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{52}}$ | = | $\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{53}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{54}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{55}}$ | = | $y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{56}}$ | = | $- y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B III |
| $\mathbf{B_{57}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{58}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{59}}$ | = | $- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{60}}$ | = | $\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{61}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{62}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{63}}$ | = | $y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{64}}$ | = | $- y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B IV |
| $\mathbf{B_{65}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{66}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{67}}$ | = | $- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{68}}$ | = | $\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{69}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{70}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{71}}$ | = | $y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{72}}$ | = | $- y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B V |
| $\mathbf{B_{73}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{74}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{75}}$ | = | $- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{76}}$ | = | $\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{77}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{78}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{79}}$ | = | $y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{80}}$ | = | $- y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VI |
| $\mathbf{B_{81}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{82}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{83}}$ | = | $- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{84}}$ | = | $\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{85}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{86}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{87}}$ | = | $y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{88}}$ | = | $- y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VII |
| $\mathbf{B_{89}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{90}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{91}}$ | = | $- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{92}}$ | = | $\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{93}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{94}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{95}}$ | = | $y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{96}}$ | = | $- y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B VIII |
| $\mathbf{B_{97}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{98}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{99}}$ | = | $- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{100}}$ | = | $\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{101}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{102}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{103}}$ | = | $y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{104}}$ | = | $- y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B IX |
| $\mathbf{B_{105}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{106}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{107}}$ | = | $- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{108}}$ | = | $\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{109}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{110}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{111}}$ | = | $y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{112}}$ | = | $- y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B X |
| $\mathbf{B_{113}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{114}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{115}}$ | = | $- \left(y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{116}}$ | = | $\left(y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{117}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{16} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{118}}$ | = | $\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{119}}$ | = | $y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{120}}$ | = | $- y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XI |
| $\mathbf{B_{121}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{122}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{123}}$ | = | $- \left(y_{17} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{17} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{124}}$ | = | $\left(y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{17} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{125}}$ | = | $- \left(x_{17} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{17} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{17} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{126}}$ | = | $\left(x_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{17} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{17} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{127}}$ | = | $y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{128}}$ | = | $- y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XII |
| $\mathbf{B_{129}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{130}}$ | = | $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{131}}$ | = | $- \left(y_{18} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{18} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{18} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{18} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{132}}$ | = | $\left(y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{18} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{18} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{18} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{133}}$ | = | $- \left(x_{18} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{18} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{18} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{18} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{134}}$ | = | $\left(x_{18} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{18} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{18} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{18} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{135}}$ | = | $y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{136}}$ | = | $- y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIII |
| $\mathbf{B_{137}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{138}}$ | = | $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{139}}$ | = | $- \left(y_{19} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{19} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{19} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{19} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{140}}$ | = | $\left(y_{19} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{19} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{19} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{19} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{141}}$ | = | $- \left(x_{19} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{19} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{19} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{19} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{19} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{142}}$ | = | $\left(x_{19} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{19} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{19} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{19} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{143}}$ | = | $y_{19} \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $a y_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{144}}$ | = | $- y_{19} \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIV |
| $\mathbf{B_{145}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{146}}$ | = | $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{147}}$ | = | $- \left(y_{20} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{20} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{20} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{20} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{148}}$ | = | $\left(y_{20} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{20} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{20} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{20} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{149}}$ | = | $- \left(x_{20} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{20} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{20} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{20} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{20} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{150}}$ | = | $\left(x_{20} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{20} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{20} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{20} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{151}}$ | = | $y_{20} \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $a y_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{152}}$ | = | $- y_{20} \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XV |
| $\mathbf{B_{153}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}+a y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{154}}$ | = | $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}- a y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{155}}$ | = | $- \left(y_{21} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{21} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{21} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{21} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{156}}$ | = | $\left(y_{21} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{21} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{21} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{21} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{157}}$ | = | $- \left(x_{21} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{21} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{21} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{21} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{21} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{158}}$ | = | $\left(x_{21} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{21} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{21} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{21} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{159}}$ | = | $y_{21} \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $a y_{21} \,\mathbf{\hat{x}}+a x_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{160}}$ | = | $- y_{21} \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{21} \,\mathbf{\hat{x}}- a x_{21} \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVI |
| $\mathbf{B_{161}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}+a y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{162}}$ | = | $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}- a y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{163}}$ | = | $- \left(y_{22} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{22} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{22} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{22} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{164}}$ | = | $\left(y_{22} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{22} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{22} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{22} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{165}}$ | = | $- \left(x_{22} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{22} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{22} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{22} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{22} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{166}}$ | = | $\left(x_{22} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{22} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{22} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{22} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{167}}$ | = | $y_{22} \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $a y_{22} \,\mathbf{\hat{x}}+a x_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{168}}$ | = | $- y_{22} \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{22} \,\mathbf{\hat{x}}- a x_{22} \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVII |
| $\mathbf{B_{169}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}+a y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{170}}$ | = | $- x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}- a y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{171}}$ | = | $- \left(y_{23} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{23} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{23} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{23} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{172}}$ | = | $\left(y_{23} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{23} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{23} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{23} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{173}}$ | = | $- \left(x_{23} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{23} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{23} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{23} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{23} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{174}}$ | = | $\left(x_{23} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{23} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{23} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{23} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{23} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{175}}$ | = | $y_{23} \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $a y_{23} \,\mathbf{\hat{x}}+a x_{23} \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{176}}$ | = | $- y_{23} \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}- \left(z_{23} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{23} \,\mathbf{\hat{x}}- a x_{23} \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XVIII |
| $\mathbf{B_{177}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}+a y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{178}}$ | = | $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}- a y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{179}}$ | = | $- \left(y_{24} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{24} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{24} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{24} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{180}}$ | = | $\left(y_{24} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{24} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{24} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{24} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{181}}$ | = | $- \left(x_{24} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{24} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{24} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{24} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{24} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{182}}$ | = | $\left(x_{24} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{24} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{24} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{24} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{24} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{183}}$ | = | $y_{24} \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $a y_{24} \,\mathbf{\hat{x}}+a x_{24} \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{184}}$ | = | $- y_{24} \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}- \left(z_{24} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{24} \,\mathbf{\hat{x}}- a x_{24} \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XIX |
| $\mathbf{B_{185}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}+a y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{186}}$ | = | $- x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}- a y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{187}}$ | = | $- \left(y_{25} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{25} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{25} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{25} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{188}}$ | = | $\left(y_{25} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{25} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{25} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{25} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{189}}$ | = | $- \left(x_{25} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{25} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{25} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{25} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{25} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{25} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{190}}$ | = | $\left(x_{25} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{25} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{25} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{25} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{25} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{25} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{191}}$ | = | $y_{25} \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $a y_{25} \,\mathbf{\hat{x}}+a x_{25} \,\mathbf{\hat{y}}- c z_{25} \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{192}}$ | = | $- y_{25} \, \mathbf{a}_{1}- x_{25} \, \mathbf{a}_{2}- \left(z_{25} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{25} \,\mathbf{\hat{x}}- a x_{25} \,\mathbf{\hat{y}}- c \left(z_{25} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XX |
| $\mathbf{B_{193}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}+a y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{194}}$ | = | $- x_{26} \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}- a y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{195}}$ | = | $- \left(y_{26} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{26} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{26} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{26} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{196}}$ | = | $\left(y_{26} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{26} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{26} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{26} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{197}}$ | = | $- \left(x_{26} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{26} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{26} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{26} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{26} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{26} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{198}}$ | = | $\left(x_{26} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{26} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{26} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{26} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{26} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{26} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{199}}$ | = | $y_{26} \, \mathbf{a}_{1}+x_{26} \, \mathbf{a}_{2}- z_{26} \, \mathbf{a}_{3}$ | = | $a y_{26} \,\mathbf{\hat{x}}+a x_{26} \,\mathbf{\hat{y}}- c z_{26} \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{200}}$ | = | $- y_{26} \, \mathbf{a}_{1}- x_{26} \, \mathbf{a}_{2}- \left(z_{26} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{26} \,\mathbf{\hat{x}}- a x_{26} \,\mathbf{\hat{y}}- c \left(z_{26} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXI |
| $\mathbf{B_{201}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $a x_{27} \,\mathbf{\hat{x}}+a y_{27} \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{202}}$ | = | $- x_{27} \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{27} \,\mathbf{\hat{x}}- a y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{203}}$ | = | $- \left(y_{27} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{27} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{27} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{27} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{27} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{204}}$ | = | $\left(y_{27} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{27} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{27} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{27} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{205}}$ | = | $- \left(x_{27} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{27} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{27} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{27} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{27} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{27} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{206}}$ | = | $\left(x_{27} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{27} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{27} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{27} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{27} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{27} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{207}}$ | = | $y_{27} \, \mathbf{a}_{1}+x_{27} \, \mathbf{a}_{2}- z_{27} \, \mathbf{a}_{3}$ | = | $a y_{27} \,\mathbf{\hat{x}}+a x_{27} \,\mathbf{\hat{y}}- c z_{27} \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{208}}$ | = | $- y_{27} \, \mathbf{a}_{1}- x_{27} \, \mathbf{a}_{2}- \left(z_{27} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{27} \,\mathbf{\hat{x}}- a x_{27} \,\mathbf{\hat{y}}- c \left(z_{27} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXII |
| $\mathbf{B_{209}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $a x_{28} \,\mathbf{\hat{x}}+a y_{28} \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{210}}$ | = | $- x_{28} \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{28} \,\mathbf{\hat{x}}- a y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{211}}$ | = | $- \left(y_{28} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{28} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{28} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{28} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{28} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{212}}$ | = | $\left(y_{28} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{28} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{28} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{28} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{213}}$ | = | $- \left(x_{28} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{28} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{28} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{28} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(y_{28} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{28} - \frac{3}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{214}}$ | = | $\left(x_{28} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{28} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{28} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{28} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(y_{28} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{28} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{215}}$ | = | $y_{28} \, \mathbf{a}_{1}+x_{28} \, \mathbf{a}_{2}- z_{28} \, \mathbf{a}_{3}$ | = | $a y_{28} \,\mathbf{\hat{x}}+a x_{28} \,\mathbf{\hat{y}}- c z_{28} \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
| $\mathbf{B_{216}}$ | = | $- y_{28} \, \mathbf{a}_{1}- x_{28} \, \mathbf{a}_{2}- \left(z_{28} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{28} \,\mathbf{\hat{x}}- a x_{28} \,\mathbf{\hat{y}}- c \left(z_{28} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8b) | B XXIII |
References
- I. Higashi, Crystal Chemistry of α-AlB$_{12}$ and γ-AlB$_{12}$, J. Solid State Chem. 154, 168–176 (2000), doi:10.1006/jssc.2000.8831.
Prototype Generator
aflow --proto=A5B22_tP216_96_5b_2a21b --params=$a,c/a,x_{1},x_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28}$