Hexagonal Trinepheline (NaAlSiO$_{4}$) Structure: ABC4D_hP168_169_4a_4a_16a_4a-001
| Prototype | AlNaO$_{4}$Si |
| AFLOW prototype label | ABC4D_hP168_169_4a_4a_16a_4a-001 |
| Mineral name | trinepheline |
| ICSD | 85553 |
| CCDC | 1645477 |
| Pearson symbol | hP168 |
| Space group number | 169 |
| Space group symbol | $P6_1$ |
| AFLOW prototype command |
aflow --proto=ABC4D_hP168_169_4a_4a_16a_4a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}$ |
- NaAlSiO$_{4}$ can be found in a variety of structures, depending upon the conditions of its formation.
- Hexagonal forms include:
- trinepheline (this structure) and
- sodium-nepheline.
- This sample was prepared by slow cooling from $≈ 1000^\circ$C.
- This structure may also be found in the enantiomorphic space group $P6_{5}$ #170.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} + y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{2}}$ | = | $- y_{1} \, \mathbf{a}_{1}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - 2 y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{1} - y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{1} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{1} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} + y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{5}}$ | = | $y_{1} \, \mathbf{a}_{1}- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{1} + 2 y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{1} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{6}}$ | = | $\left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{1} - y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Al I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} + y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{8}}$ | = | $- y_{2} \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - 2 y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{2} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{2} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} + y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{11}}$ | = | $y_{2} \, \mathbf{a}_{1}- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{2} + 2 y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{2} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{12}}$ | = | $\left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{2} - y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Al II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{14}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{3} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{16}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{17}}$ | = | $y_{3} \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{3} + 2 y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{3} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{18}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Al III |
| $\mathbf{B_{19}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{20}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{21}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{4} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{22}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{23}}$ | = | $y_{4} \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{4} + 2 y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{4} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{24}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Al IV |
| $\mathbf{B_{25}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{26}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{27}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{5} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{28}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{29}}$ | = | $y_{5} \, \mathbf{a}_{1}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{5} + 2 y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{5} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{30}}$ | = | $\left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Na I |
| $\mathbf{B_{31}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{32}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{6} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{34}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{35}}$ | = | $y_{6} \, \mathbf{a}_{1}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{6} + 2 y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{6} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{36}}$ | = | $\left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Na II |
| $\mathbf{B_{37}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{38}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{39}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{7} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{40}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{41}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{7} + 2 y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{7} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{42}}$ | = | $\left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Na III |
| $\mathbf{B_{43}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{44}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{45}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{8} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{46}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{47}}$ | = | $y_{8} \, \mathbf{a}_{1}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{8} + 2 y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{8} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{48}}$ | = | $\left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Na IV |
| $\mathbf{B_{49}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{50}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{51}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{9} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{52}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{53}}$ | = | $y_{9} \, \mathbf{a}_{1}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{9} + 2 y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{9} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{54}}$ | = | $\left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O I |
| $\mathbf{B_{55}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{56}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{57}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{10} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{58}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{59}}$ | = | $y_{10} \, \mathbf{a}_{1}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{10} + 2 y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{10} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{60}}$ | = | $\left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O II |
| $\mathbf{B_{61}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{62}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - 2 y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{63}}$ | = | $- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{11} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{64}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{65}}$ | = | $y_{11} \, \mathbf{a}_{1}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{11} + 2 y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{11} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{66}}$ | = | $\left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O III |
| $\mathbf{B_{67}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{68}}$ | = | $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{69}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{12} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{70}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{71}}$ | = | $y_{12} \, \mathbf{a}_{1}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{12} + 2 y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{12} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{72}}$ | = | $\left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O IV |
| $\mathbf{B_{73}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{74}}$ | = | $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{75}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{13} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{76}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{77}}$ | = | $y_{13} \, \mathbf{a}_{1}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{13} + 2 y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{13} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{78}}$ | = | $\left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O V |
| $\mathbf{B_{79}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{80}}$ | = | $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - 2 y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{81}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{14} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{82}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{83}}$ | = | $y_{14} \, \mathbf{a}_{1}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{14} + 2 y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{14} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{84}}$ | = | $\left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O VI |
| $\mathbf{B_{85}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{86}}$ | = | $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{87}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{15} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{88}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{89}}$ | = | $y_{15} \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{15} + 2 y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{15} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{90}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O VII |
| $\mathbf{B_{91}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{92}}$ | = | $- y_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{93}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{16} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{94}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{95}}$ | = | $y_{16} \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{16} + 2 y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{16} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{96}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O VIII |
| $\mathbf{B_{97}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{98}}$ | = | $- y_{17} \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} - 2 y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{99}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{17} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{100}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{101}}$ | = | $y_{17} \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{17} + 2 y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{17} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{102}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O IX |
| $\mathbf{B_{103}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{104}}$ | = | $- y_{18} \, \mathbf{a}_{1}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} - 2 y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{105}}$ | = | $- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{18} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{106}}$ | = | $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{107}}$ | = | $y_{18} \, \mathbf{a}_{1}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{18} + 2 y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{18} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{108}}$ | = | $\left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O X |
| $\mathbf{B_{109}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{19} + y_{19}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{19} - y_{19}\right) \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{110}}$ | = | $- y_{19} \, \mathbf{a}_{1}+\left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{19} - 2 y_{19}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{111}}$ | = | $- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}- x_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{19} - y_{19}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{19} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{19} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{112}}$ | = | $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{19} + y_{19}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{19} - y_{19}\right) \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{113}}$ | = | $y_{19} \, \mathbf{a}_{1}- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{19} + 2 y_{19}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{19} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{19} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{114}}$ | = | $\left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}+x_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{19} - y_{19}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XI |
| $\mathbf{B_{115}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{20} + y_{20}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{20} - y_{20}\right) \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{116}}$ | = | $- y_{20} \, \mathbf{a}_{1}+\left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{20} - 2 y_{20}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{117}}$ | = | $- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}- x_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{20} - y_{20}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{20} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{20} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{118}}$ | = | $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{20} + y_{20}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{20} - y_{20}\right) \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{119}}$ | = | $y_{20} \, \mathbf{a}_{1}- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{20} + 2 y_{20}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{20} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{20} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{120}}$ | = | $\left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}+x_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{20} - y_{20}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XII |
| $\mathbf{B_{121}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{21} + y_{21}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{21} - y_{21}\right) \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{122}}$ | = | $- y_{21} \, \mathbf{a}_{1}+\left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{21} - 2 y_{21}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{123}}$ | = | $- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}- x_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{21} - y_{21}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{21} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{21} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{124}}$ | = | $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{21} + y_{21}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{21} - y_{21}\right) \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{125}}$ | = | $y_{21} \, \mathbf{a}_{1}- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{21} + 2 y_{21}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{21} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{21} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{126}}$ | = | $\left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}+x_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{21} - y_{21}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIII |
| $\mathbf{B_{127}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{22} + y_{22}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{22} - y_{22}\right) \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{128}}$ | = | $- y_{22} \, \mathbf{a}_{1}+\left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{22} - 2 y_{22}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{129}}$ | = | $- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}- x_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{22} - y_{22}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{22} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{22} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{130}}$ | = | $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{22} + y_{22}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{22} - y_{22}\right) \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{131}}$ | = | $y_{22} \, \mathbf{a}_{1}- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{22} + 2 y_{22}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{22} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{22} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{132}}$ | = | $\left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}+x_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{22} - y_{22}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XIV |
| $\mathbf{B_{133}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{23} + y_{23}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{23} - y_{23}\right) \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{134}}$ | = | $- y_{23} \, \mathbf{a}_{1}+\left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{23} - 2 y_{23}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{135}}$ | = | $- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}- x_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{23} - y_{23}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{23} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{23} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{136}}$ | = | $- x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{23} + y_{23}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{23} - y_{23}\right) \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{137}}$ | = | $y_{23} \, \mathbf{a}_{1}- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{23} + 2 y_{23}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{23} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{23} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{138}}$ | = | $\left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}+x_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{23} - y_{23}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XV |
| $\mathbf{B_{139}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{140}}$ | = | $- y_{24} \, \mathbf{a}_{1}+\left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{24} - 2 y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{141}}$ | = | $- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}- x_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{24} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{142}}$ | = | $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{24} + y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{24} - y_{24}\right) \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{143}}$ | = | $y_{24} \, \mathbf{a}_{1}- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{24} + 2 y_{24}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{24} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{24} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{144}}$ | = | $\left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}+x_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{24} - y_{24}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | O XVI |
| $\mathbf{B_{145}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{146}}$ | = | $- y_{25} \, \mathbf{a}_{1}+\left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{25} - 2 y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{147}}$ | = | $- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}- x_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{25} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{148}}$ | = | $- x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{25} + y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{25} - y_{25}\right) \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{149}}$ | = | $y_{25} \, \mathbf{a}_{1}- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{25} + 2 y_{25}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{25} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{25} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{150}}$ | = | $\left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}+x_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{25} - y_{25}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Si I |
| $\mathbf{B_{151}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{26} + y_{26}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{26} - y_{26}\right) \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{152}}$ | = | $- y_{26} \, \mathbf{a}_{1}+\left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{26} - 2 y_{26}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{153}}$ | = | $- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}- x_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{26} - y_{26}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{26} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{26} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{154}}$ | = | $- x_{26} \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{26} + y_{26}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{26} - y_{26}\right) \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{155}}$ | = | $y_{26} \, \mathbf{a}_{1}- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{26} + 2 y_{26}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{26} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{26} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{156}}$ | = | $\left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}+x_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{26} - y_{26}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Si II |
| $\mathbf{B_{157}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{27} + y_{27}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{27} - y_{27}\right) \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{158}}$ | = | $- y_{27} \, \mathbf{a}_{1}+\left(x_{27} - y_{27}\right) \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{27} - 2 y_{27}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{159}}$ | = | $- \left(x_{27} - y_{27}\right) \, \mathbf{a}_{1}- x_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{27} - y_{27}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{27} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{27} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{160}}$ | = | $- x_{27} \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{27} + y_{27}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{27} - y_{27}\right) \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{161}}$ | = | $y_{27} \, \mathbf{a}_{1}- \left(x_{27} - y_{27}\right) \, \mathbf{a}_{2}+\left(z_{27} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{27} + 2 y_{27}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{27} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{27} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{162}}$ | = | $\left(x_{27} - y_{27}\right) \, \mathbf{a}_{1}+x_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{27} - y_{27}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Si III |
| $\mathbf{B_{163}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{28} + y_{28}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{28} - y_{28}\right) \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ | (6a) | Si IV |
| $\mathbf{B_{164}}$ | = | $- y_{28} \, \mathbf{a}_{1}+\left(x_{28} - y_{28}\right) \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{28} - 2 y_{28}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (6a) | Si IV |
| $\mathbf{B_{165}}$ | = | $- \left(x_{28} - y_{28}\right) \, \mathbf{a}_{1}- x_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{28} - y_{28}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{28} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{28} + 2\right) \,\mathbf{\hat{z}}$ | (6a) | Si IV |
| $\mathbf{B_{166}}$ | = | $- x_{28} \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{28} + y_{28}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{28} - y_{28}\right) \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6a) | Si IV |
| $\mathbf{B_{167}}$ | = | $y_{28} \, \mathbf{a}_{1}- \left(x_{28} - y_{28}\right) \, \mathbf{a}_{2}+\left(z_{28} + \frac{5}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{28} + 2 y_{28}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{28} \,\mathbf{\hat{y}}+\frac{1}{6}c \left(6 z_{28} + 5\right) \,\mathbf{\hat{z}}$ | (6a) | Si IV |
| $\mathbf{B_{168}}$ | = | $\left(x_{28} - y_{28}\right) \, \mathbf{a}_{1}+x_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{6}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{28} - y_{28}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{6}\right) \,\mathbf{\hat{z}}$ | (6a) | Si IV |
References
- V. Kahlenberg and H. Böhm, Crystal structure of hexagonal trinepheline – A new synthetic NaAlSiO$_{4}$ modification, Am. Mineral. 83, 631–637 (1998).
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=ABC4D_hP168_169_4a_4a_16a_4a --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28}$