Sr$_{8}$Os$_{6.3}$O$_{24}$ Structure: A36B11C12_hP118_185_4c4d_a2b2c_ab3c-001
| Prototype | O$_{24}$Os$_{6.3}$Sr$_{8}$ |
| AFLOW prototype label | A36B11C12_hP118_185_4c4d_a2b2c_ab3c-001 |
| ICSD | 112868 |
| Pearson symbol | hP118 |
| Space group number | 185 |
| Space group symbol | $P6_3cm$ |
| AFLOW prototype command |
aflow --proto=A36B11C12_hP118_185_4c4d_a2b2c_ab3c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}$ |
- The first osmium (4b) site (Os-II) has an occupancy of 93.1%, while the next (4b) site (Os-III) has 27.9% occupancy.
- Space group $P6_{3}cm$ does not specify the origin of the $z$ axis, we follow (Thakur, 2021) and set $z_{2} = 0$ for the Sr-I atom.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Os I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Os I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Sr I |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Sr I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Os II |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Os II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Os II |
| $\mathbf{B_{8}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4b) | Os II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Os III |
| $\mathbf{B_{10}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Os III |
| $\mathbf{B_{11}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Os III |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4b) | Os III |
| $\mathbf{B_{13}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | Sr II |
| $\mathbf{B_{14}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Sr II |
| $\mathbf{B_{15}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4b) | Sr II |
| $\mathbf{B_{16}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | Sr II |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{18}}$ | = | $x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{19}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{20}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{21}}$ | = | $- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{6} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{22}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O I |
| $\mathbf{B_{23}}$ | = | $x_{7} \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{24}}$ | = | $x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{25}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+c z_{7} \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{26}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{27}}$ | = | $- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{7} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{28}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O II |
| $\mathbf{B_{29}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{30}}$ | = | $x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{31}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{32}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{8} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{33}}$ | = | $- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{8} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{34}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O III |
| $\mathbf{B_{35}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{36}}$ | = | $x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{37}}$ | = | $- x_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{38}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{9} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{39}}$ | = | $- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{9} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{40}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | O IV |
| $\mathbf{B_{41}}$ | = | $x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{42}}$ | = | $x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{43}}$ | = | $- x_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{44}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{10} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{45}}$ | = | $- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{10} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{46}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os IV |
| $\mathbf{B_{47}}$ | = | $x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{48}}$ | = | $x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{49}}$ | = | $- x_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{50}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{11} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{51}}$ | = | $- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{11} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{52}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Os V |
| $\mathbf{B_{53}}$ | = | $x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{12} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{54}}$ | = | $x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{12} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{55}}$ | = | $- x_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{56}}$ | = | $- x_{12} \, \mathbf{a}_{1}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{12} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{57}}$ | = | $- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{12} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{58}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr III |
| $\mathbf{B_{59}}$ | = | $x_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{13} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{60}}$ | = | $x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{13} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{61}}$ | = | $- x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+c z_{13} \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{62}}$ | = | $- x_{13} \, \mathbf{a}_{1}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{13} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{63}}$ | = | $- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{13} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{64}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr IV |
| $\mathbf{B_{65}}$ | = | $x_{14} \, \mathbf{a}_{1}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{14} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{66}}$ | = | $x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{14} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{67}}$ | = | $- x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+c z_{14} \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{68}}$ | = | $- x_{14} \, \mathbf{a}_{1}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{14} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{69}}$ | = | $- x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a x_{14} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{70}}$ | = | $x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (6c) | Sr V |
| $\mathbf{B_{71}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{72}}$ | = | $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{73}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{74}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{75}}$ | = | $y_{15} \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{15} + 2 y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{76}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{77}}$ | = | $- y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{78}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{15} + 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{79}}$ | = | $x_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{80}}$ | = | $y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{81}}$ | = | $\left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{82}}$ | = | $- x_{15} \, \mathbf{a}_{1}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (12d) | O V |
| $\mathbf{B_{83}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{84}}$ | = | $- y_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{85}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{86}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{87}}$ | = | $y_{16} \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{16} + 2 y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{88}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{89}}$ | = | $- y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{90}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{16} + 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{91}}$ | = | $x_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{92}}$ | = | $y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{93}}$ | = | $\left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{94}}$ | = | $- x_{16} \, \mathbf{a}_{1}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (12d) | O VI |
| $\mathbf{B_{95}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{96}}$ | = | $- y_{17} \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} - 2 y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{97}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{98}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{99}}$ | = | $y_{17} \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{17} + 2 y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{100}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{101}}$ | = | $- y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{102}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{17} + 2 y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{103}}$ | = | $x_{17} \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{104}}$ | = | $y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} + y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{17} - y_{17}\right) \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{105}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{17} - 2 y_{17}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{106}}$ | = | $- x_{17} \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{17} - y_{17}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (12d) | O VII |
| $\mathbf{B_{107}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{108}}$ | = | $- y_{18} \, \mathbf{a}_{1}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} - 2 y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{109}}$ | = | $- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{110}}$ | = | $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{111}}$ | = | $y_{18} \, \mathbf{a}_{1}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{18} + 2 y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{112}}$ | = | $\left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{113}}$ | = | $- y_{18} \, \mathbf{a}_{1}- x_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{114}}$ | = | $- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(- x_{18} + 2 y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{115}}$ | = | $x_{18} \, \mathbf{a}_{1}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{116}}$ | = | $y_{18} \, \mathbf{a}_{1}+x_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} + y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \left(x_{18} - y_{18}\right) \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{117}}$ | = | $\left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{18} - 2 y_{18}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
| $\mathbf{B_{118}}$ | = | $- x_{18} \, \mathbf{a}_{1}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{18} - y_{18}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (12d) | O VIII |
References
- G. S. Thakur, T. Doert, S. Mohitkar, W. Schnelle, C. Felser, and M. Jansen, Crystal Growth of a New 8H Perovskite Sr$_{8}$Os$_{6.3}$O$_{24}$ Exhibiting High T$_{c}$ Ferromagnetism, Cryst. Growth Des. 21, 2459–2464 (2021), doi:10.1021/acs.cgd.1c00057.
Prototype Generator
aflow --proto=A36B11C12_hP118_185_4c4d_a2b2c_ab3c --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},x_{6},z_{6},x_{7},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18}$