β-B (R-105) Structure: A_hR105_166_ac9h4i-001
| Prototype | B |
| AFLOW prototype label | A_hR105_166_ac9h4i-001 |
| ICSD | 14288 |
| Pearson symbol | hR105 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A_hR105_166_ac9h4i-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}$ |
- This is apparently the ground state of boron, with 105 atoms in the unit cell.
- (Donohue, 1982) gives two possible sets of internal coordinates for the atoms on page 64. We use the second set (Geist, 1970), as it has no partially filled sites.
- Note the relationship between the icosahedra in this structure, $\alpha$–B and T-50 B.
- Hexagonal settings for rhombohedral structures can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | B I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | B II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{7}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{9}}$ | = | $- x_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6h) | B III |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{11}}$ | = | $z_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{12}}$ | = | $x_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{13}}$ | = | $- z_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{14}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{4} - z_{4}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{4} + z_{4}\right) \,\mathbf{\hat{z}}$ | (6h) | B IV |
| $\mathbf{B_{16}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{17}}$ | = | $z_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{18}}$ | = | $x_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{19}}$ | = | $- z_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{20}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{21}}$ | = | $- x_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{5} - z_{5}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{5} + z_{5}\right) \,\mathbf{\hat{z}}$ | (6h) | B V |
| $\mathbf{B_{22}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{23}}$ | = | $z_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{24}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{25}}$ | = | $- z_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{26}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{27}}$ | = | $- x_{6} \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{6} - z_{6}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{6} + z_{6}\right) \,\mathbf{\hat{z}}$ | (6h) | B VI |
| $\mathbf{B_{28}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{29}}$ | = | $z_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{30}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{31}}$ | = | $- z_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{32}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{33}}$ | = | $- x_{7} \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- x_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{7} - z_{7}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{7} + z_{7}\right) \,\mathbf{\hat{z}}$ | (6h) | B VII |
| $\mathbf{B_{34}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{35}}$ | = | $z_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{36}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{37}}$ | = | $- z_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{38}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{39}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- x_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{8} - z_{8}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{8} + z_{8}\right) \,\mathbf{\hat{z}}$ | (6h) | B VIII |
| $\mathbf{B_{40}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{41}}$ | = | $z_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{42}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{43}}$ | = | $- z_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{44}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{45}}$ | = | $- x_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- x_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{9} - z_{9}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{9} + z_{9}\right) \,\mathbf{\hat{z}}$ | (6h) | B IX |
| $\mathbf{B_{46}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{47}}$ | = | $z_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{48}}$ | = | $x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{49}}$ | = | $- z_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{50}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{51}}$ | = | $- x_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{2}- x_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{10} - z_{10}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{10} + z_{10}\right) \,\mathbf{\hat{z}}$ | (6h) | B X |
| $\mathbf{B_{52}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{53}}$ | = | $z_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{54}}$ | = | $x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{\sqrt{3}}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{55}}$ | = | $- z_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{56}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{57}}$ | = | $- x_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{2}- x_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{\sqrt{3}}a \left(x_{11} - z_{11}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(2 x_{11} + z_{11}\right) \,\mathbf{\hat{z}}$ | (6h) | B XI |
| $\mathbf{B_{58}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{59}}$ | = | $z_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{60}}$ | = | $y_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{61}}$ | = | $- z_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{62}}$ | = | $- y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{63}}$ | = | $- x_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{64}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{65}}$ | = | $- z_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- y_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{66}}$ | = | $- y_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{2}- x_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{67}}$ | = | $z_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} - z_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} - 2 y_{12} + z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{68}}$ | = | $y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{12} - z_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{12} - y_{12} - z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{69}}$ | = | $x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{2}+y_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{12} + y_{12} - 2 z_{12}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{12} + y_{12} + z_{12}\right) \,\mathbf{\hat{z}}$ | (12i) | B XII |
| $\mathbf{B_{70}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{71}}$ | = | $z_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{72}}$ | = | $y_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{73}}$ | = | $- z_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{74}}$ | = | $- y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{75}}$ | = | $- x_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{76}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{77}}$ | = | $- z_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- y_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{78}}$ | = | $- y_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{79}}$ | = | $z_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} - z_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} - 2 y_{13} + z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{80}}$ | = | $y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{13} - z_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{13} - y_{13} - z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{81}}$ | = | $x_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{2}+y_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{13} + y_{13} - 2 z_{13}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{13} + y_{13} + z_{13}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIII |
| $\mathbf{B_{82}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{83}}$ | = | $z_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{84}}$ | = | $y_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{85}}$ | = | $- z_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{86}}$ | = | $- y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{87}}$ | = | $- x_{14} \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{88}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{89}}$ | = | $- z_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- y_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{90}}$ | = | $- y_{14} \, \mathbf{a}_{1}- z_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{91}}$ | = | $z_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} - z_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} - 2 y_{14} + z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{92}}$ | = | $y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{14} - z_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{14} - y_{14} - z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{93}}$ | = | $x_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{2}+y_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{14} + y_{14} - 2 z_{14}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{14} + y_{14} + z_{14}\right) \,\mathbf{\hat{z}}$ | (12i) | B XIV |
| $\mathbf{B_{94}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - z_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{15} - 2 y_{15} + z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{95}}$ | = | $z_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+y_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{15} - z_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{15} - y_{15} - z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{96}}$ | = | $y_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+x_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{15} + y_{15} - 2 z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{97}}$ | = | $- z_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- x_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - z_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{15} - 2 y_{15} + z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{98}}$ | = | $- y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{15} - z_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{15} - y_{15} - z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{99}}$ | = | $- x_{15} \, \mathbf{a}_{1}- z_{15} \, \mathbf{a}_{2}- y_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{15} + y_{15} - 2 z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{100}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} - z_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{15} - 2 y_{15} + z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{101}}$ | = | $- z_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- y_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{15} - z_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{15} - y_{15} - z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{102}}$ | = | $- y_{15} \, \mathbf{a}_{1}- z_{15} \, \mathbf{a}_{2}- x_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{15} + y_{15} - 2 z_{15}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{103}}$ | = | $z_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+x_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} - z_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{15} - 2 y_{15} + z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{104}}$ | = | $y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{15} - z_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{15} - y_{15} - z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
| $\mathbf{B_{105}}$ | = | $x_{15} \, \mathbf{a}_{1}+z_{15} \, \mathbf{a}_{2}+y_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{15} + y_{15} - 2 z_{15}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{15} + y_{15} + z_{15}\right) \,\mathbf{\hat{z}}$ | (12i) | B XV |
References
- D. Geist, R. Kloss, and H. Follner, Verfeinerung des β-rhomboedrischen Bors, Acta Crystallogr. Sect. B 26, 1800–1804 (1970), doi:10.1107/S0567740870004910.
Found in
- J. Donohue, The Structures of the Elements (Robert E. Krieger Publishing Company, New York, 1974).
Prototype Generator
aflow --proto=A_hR105_166_ac9h4i --params=$a,c/a,x_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15}$