Nb$_{7}$Rh$_{6}$B$_{8}$ Structure: A8B7C6_hP126_176_2h3i_acd6h_3i-001
| Prototype | B$_{8}$Nb$_{7}$Rh$_{6}$ |
| AFLOW prototype label | A8B7C6_hP126_176_2h3i_acd6h_3i-001 |
| ICSD | 263043 |
| Pearson symbol | hP126 |
| Space group number | 176 |
| Space group symbol | $P6_3/m$ |
| AFLOW prototype command |
aflow --proto=A8B7C6_hP126_176_2h3i_acd6h_3i-001
--params=$a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}$ |
Other compounds with this structure
Ta$_{7}$Rh$_{6}$B$_{8}$
- (Zheng, 2012) place the Nb-I (their Nb3) atom on the (2b) Wyckoff position, but give the coordinates for the (2a) position. We assume that the coordinates are correct. This assessment agrees with the ICSD entry.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2a) | Nb I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2a) | Nb I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Nb II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Nb II |
| $\mathbf{B_{5}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2d) | Nb III |
| $\mathbf{B_{6}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2d) | Nb III |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{8}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{11}}$ | = | $y_{4} \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{4} + 2 y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B I |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{14}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{15}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{16}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{17}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{5} + 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | B II |
| $\mathbf{B_{19}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{20}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{21}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{22}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{23}}$ | = | $y_{6} \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{6} + 2 y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{24}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IV |
| $\mathbf{B_{25}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{26}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{27}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{28}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{29}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{30}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb V |
| $\mathbf{B_{31}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{32}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{33}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{34}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{35}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{36}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VI |
| $\mathbf{B_{37}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{38}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{39}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{40}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{41}}$ | = | $y_{9} \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{9} + 2 y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{42}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VII |
| $\mathbf{B_{43}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{44}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{45}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{46}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{47}}$ | = | $y_{10} \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{10} + 2 y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{48}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb VIII |
| $\mathbf{B_{49}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{50}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - 2 y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{51}}$ | = | $- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{52}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{53}}$ | = | $y_{11} \, \mathbf{a}_{1}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{11} + 2 y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{54}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (6h) | Nb IX |
| $\mathbf{B_{55}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{56}}$ | = | $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{57}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{58}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{59}}$ | = | $y_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{12} + 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{60}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{61}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{62}}$ | = | $y_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{12} + 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{63}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{64}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{65}}$ | = | $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{66}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B III |
| $\mathbf{B_{67}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{68}}$ | = | $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{69}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{70}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{71}}$ | = | $y_{13} \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{13} + 2 y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{72}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{73}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{74}}$ | = | $y_{13} \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{13} + 2 y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{75}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{76}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{77}}$ | = | $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{78}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B IV |
| $\mathbf{B_{79}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{80}}$ | = | $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - 2 y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{81}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{82}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{83}}$ | = | $y_{14} \, \mathbf{a}_{1}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{14} + 2 y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{84}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{85}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{86}}$ | = | $y_{14} \, \mathbf{a}_{1}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{14} + 2 y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{87}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{88}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{89}}$ | = | $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - 2 y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{90}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | B V |
| $\mathbf{B_{91}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{92}}$ | = | $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{93}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{94}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{95}}$ | = | $y_{15} \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{15} + 2 y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{96}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{97}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{98}}$ | = | $y_{15} \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{15} + 2 y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{99}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{100}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{101}}$ | = | $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{102}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh I |
| $\mathbf{B_{103}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{104}}$ | = | $- y_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{105}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{106}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{107}}$ | = | $y_{16} \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{16} + 2 y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{108}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{109}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{110}}$ | = | $y_{16} \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{16} + 2 y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{111}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{112}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{113}}$ | = | $- y_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{114}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh II |
| $\mathbf{B_{115}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{116}}$ | = | $- y_{17} \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} - 2 y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{117}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{118}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{119}}$ | = | $y_{17} \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{17} + 2 y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{120}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{121}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{122}}$ | = | $y_{17} \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{17} + 2 y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{123}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{124}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{125}}$ | = | $- y_{17} \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} - 2 y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
| $\mathbf{B_{126}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12i) | Rh III |
References
- Q. Zheng, M. Kohout, R. Gumeniuk, N. Abramchuk, H. Borrmann, Y. Prots, U. Burkhardt, W. Schnelle, L. Akselrud, H. Gu, A. Leithe-Jasper, and Y. Grin, TM$_{7}$TM'$_{6}$B$_{8}$ (TM = Ta, Nb; TM' = Ru, Rh, Ir): New Compounds with [B$_{6}$] Ring Polyanions, Inorg. Chem. 51, 7492–7483 (2012), doi:10.1021/ic201978n.
Prototype Generator
aflow --proto=A8B7C6_hP126_176_2h3i_acd6h_3i --params=$a,c/a,x_{4},y_{4},x_{5},y_{5},x_{6},y_{6},x_{7},y_{7},x_{8},y_{8},x_{9},y_{9},x_{10},y_{10},x_{11},y_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17}$