Be[BH$_{4}$]$_{2}$ Structure: A2BC8_tI176_110_2b_b_8b-001
| Prototype | B$_{2}$BeH$_{8}$ |
| AFLOW prototype label | A2BC8_tI176_110_2b_b_8b-001 |
| ICSD | 10315 |
| Pearson symbol | tI176 |
| Space group number | 110 |
| Space group symbol | $I4_1cd$ |
| AFLOW prototype command |
aflow --proto=A2BC8_tI176_110_2b_b_8b-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
- Space group $I4_{1}cd$ #110 allows an arbitary placement of the $z$-axis origin, and we put a beryllium atom there by setting $z_{3} = 0$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(x_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{2}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(x_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{3}}$ | = | $\left(x_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{4}}$ | = | $\left(- x_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{1} + y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{5}}$ | = | $\left(- y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{6}}$ | = | $\left(y_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{1} + z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{7}}$ | = | $\left(- x_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{1} + y_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{8}}$ | = | $\left(x_{1} + z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{1} + y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B I |
| $\mathbf{B_{9}}$ | = | $\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{10}}$ | = | $- \left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{11}}$ | = | $\left(x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{12}}$ | = | $\left(- x_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{13}}$ | = | $\left(- y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{14}}$ | = | $\left(y_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{15}}$ | = | $\left(- x_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{16}}$ | = | $\left(x_{2} + z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | B II |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{19}}$ | = | $\left(x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{20}}$ | = | $\left(- x_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{21}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{22}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{23}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{24}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | Be I |
| $\mathbf{B_{25}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{26}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{27}}$ | = | $\left(x_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{28}}$ | = | $\left(- x_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{29}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{30}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{31}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{32}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H I |
| $\mathbf{B_{33}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{34}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{35}}$ | = | $\left(x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{36}}$ | = | $\left(- x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{37}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{38}}$ | = | $\left(y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{39}}$ | = | $\left(- x_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{40}}$ | = | $\left(x_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H II |
| $\mathbf{B_{41}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{42}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{43}}$ | = | $\left(x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{44}}$ | = | $\left(- x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{45}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{46}}$ | = | $\left(y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{47}}$ | = | $\left(- x_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{48}}$ | = | $\left(x_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H III |
| $\mathbf{B_{49}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{50}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{51}}$ | = | $\left(x_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{52}}$ | = | $\left(- x_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{53}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{54}}$ | = | $\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{55}}$ | = | $\left(- x_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{56}}$ | = | $\left(x_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H IV |
| $\mathbf{B_{57}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{58}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{59}}$ | = | $\left(x_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{60}}$ | = | $\left(- x_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{61}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{62}}$ | = | $\left(y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{63}}$ | = | $\left(- x_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{64}}$ | = | $\left(x_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H V |
| $\mathbf{B_{65}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{66}}$ | = | $- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{67}}$ | = | $\left(x_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{68}}$ | = | $\left(- x_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{69}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{70}}$ | = | $\left(y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{71}}$ | = | $\left(- x_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{72}}$ | = | $\left(x_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VI |
| $\mathbf{B_{73}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{74}}$ | = | $- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{75}}$ | = | $\left(x_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{76}}$ | = | $\left(- x_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{77}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{78}}$ | = | $\left(y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{79}}$ | = | $\left(- x_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{80}}$ | = | $\left(x_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VII |
| $\mathbf{B_{81}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{82}}$ | = | $- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{83}}$ | = | $\left(x_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{84}}$ | = | $\left(- x_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{85}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{86}}$ | = | $\left(y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{87}}$ | = | $\left(- x_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
| $\mathbf{B_{88}}$ | = | $\left(x_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16b) | H VIII |
References
- D. S. Marynick and W. N. Lipscomb, Crystal Structure of Beryllium Borohydride, Inorg. Chem. 11, 820–823 (1972), doi:10.1021/ic50110a033.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A2BC8_tI176_110_2b_b_8b --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$