Li$_{22}$Si$_{5}$ Structure: A22B5_cF432_196_abcd6efg4h_2efg-001
| Prototype | Li$_{22}$Si$_{5}$ |
| AFLOW prototype label | A22B5_cF432_196_abcd6efg4h_2efg-001 |
| ICSD | 24596 |
| Pearson symbol | cF432 |
| Space group number | 196 |
| Space group symbol | $F23$ |
| AFLOW prototype command |
aflow --proto=A22B5_cF432_196_abcd6efg4h_2efg-001
--params=$a, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak x_{10}, \allowbreak x_{11}, \allowbreak x_{12}, \allowbreak x_{13}, \allowbreak x_{14}, \allowbreak x_{15}, \allowbreak x_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}$ |
Other compounds with this structure
Li$_{22}$Ge$_{5}$, Li$_{22}$Pb$_{5}$, Li$_{22}$Sn$_{5}$, Li$_{22}$Tl$_{5}$
- The ICSD and other authorities use Li$_{22}$Pb$_{5}$ as the prototype for this structure, but (Goward, 2001) suggests that the true structure of that compound is Li$_{17}$Pb$_{4}$, changing the space group from $F32$ #196 to $F\overline{4}3m$ Li$_{22}$Si$_{5}$ as the prototype.
- This is one of the few crystal structures where all of the Wyckoff positions in its space group are occupied.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (4b) | Li II |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (4c) | Li III |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (4d) | Li IV |
| $\mathbf{B_{5}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{6}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}- 3 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{7}}$ | = | $x_{5} \, \mathbf{a}_{1}- 3 x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{8}}$ | = | $- 3 x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{9}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}- 3 x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}- 3 x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{12}}$ | = | $- 3 x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- a x_{6} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{13}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{14}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}- 3 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{15}}$ | = | $x_{7} \, \mathbf{a}_{1}- 3 x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{16}}$ | = | $- 3 x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- a x_{7} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{17}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{18}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}- 3 x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{19}}$ | = | $x_{8} \, \mathbf{a}_{1}- 3 x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{20}}$ | = | $- 3 x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- a x_{8} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{21}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{22}}$ | = | $x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}- 3 x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{23}}$ | = | $x_{9} \, \mathbf{a}_{1}- 3 x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{24}}$ | = | $- 3 x_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+x_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- a x_{9} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{25}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{26}}$ | = | $x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}- 3 x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+a x_{10} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{27}}$ | = | $x_{10} \, \mathbf{a}_{1}- 3 x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{28}}$ | = | $- 3 x_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+x_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- a x_{10} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{29}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{30}}$ | = | $x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}- 3 x_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+a x_{11} \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{31}}$ | = | $x_{11} \, \mathbf{a}_{1}- 3 x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{32}}$ | = | $- 3 x_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+x_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- a x_{11} \,\mathbf{\hat{z}}$ | (16e) | Si I |
| $\mathbf{B_{33}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ | (16e) | Si II |
| $\mathbf{B_{34}}$ | = | $x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}- 3 x_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+a x_{12} \,\mathbf{\hat{z}}$ | (16e) | Si II |
| $\mathbf{B_{35}}$ | = | $x_{12} \, \mathbf{a}_{1}- 3 x_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ | (16e) | Si II |
| $\mathbf{B_{36}}$ | = | $- 3 x_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+x_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- a x_{12} \,\mathbf{\hat{z}}$ | (16e) | Si II |
| $\mathbf{B_{37}}$ | = | $- x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}$ | (24f) | Li XI |
| $\mathbf{B_{38}}$ | = | $x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}$ | (24f) | Li XI |
| $\mathbf{B_{39}}$ | = | $x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{y}}$ | (24f) | Li XI |
| $\mathbf{B_{40}}$ | = | $- x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{y}}$ | (24f) | Li XI |
| $\mathbf{B_{41}}$ | = | $x_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}- x_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{z}}$ | (24f) | Li XI |
| $\mathbf{B_{42}}$ | = | $- x_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+x_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{z}}$ | (24f) | Li XI |
| $\mathbf{B_{43}}$ | = | $- x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}$ | (24f) | Si III |
| $\mathbf{B_{44}}$ | = | $x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}$ | (24f) | Si III |
| $\mathbf{B_{45}}$ | = | $x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{y}}$ | (24f) | Si III |
| $\mathbf{B_{46}}$ | = | $- x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{y}}$ | (24f) | Si III |
| $\mathbf{B_{47}}$ | = | $x_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}- x_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{z}}$ | (24f) | Si III |
| $\mathbf{B_{48}}$ | = | $- x_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+x_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{z}}$ | (24f) | Si III |
| $\mathbf{B_{49}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+x_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{50}}$ | = | $x_{15} \, \mathbf{a}_{1}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{51}}$ | = | $x_{15} \, \mathbf{a}_{1}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{52}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{53}}$ | = | $x_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{15} \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{54}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Li XII |
| $\mathbf{B_{55}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+x_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{56}}$ | = | $x_{16} \, \mathbf{a}_{1}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{57}}$ | = | $x_{16} \, \mathbf{a}_{1}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{58}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{59}}$ | = | $x_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+a x_{16} \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{60}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}+x_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (24g) | Si IV |
| $\mathbf{B_{61}}$ | = | $\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{62}}$ | = | $\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{63}}$ | = | $\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}- a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{64}}$ | = | $- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}- a z_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{65}}$ | = | $\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{1}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $a z_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+a y_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{66}}$ | = | $- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $a z_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- a y_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{67}}$ | = | $\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a z_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+a y_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{68}}$ | = | $\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a z_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- a y_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{69}}$ | = | $\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{2}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}+a z_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{70}}$ | = | $\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}+a z_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{71}}$ | = | $- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(- x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}- a z_{17} \,\mathbf{\hat{y}}- a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{72}}$ | = | $\left(x_{17} + y_{17} - z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - y_{17} + z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17} + z_{17}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}- a z_{17} \,\mathbf{\hat{y}}+a x_{17} \,\mathbf{\hat{z}}$ | (48h) | Li XIII |
| $\mathbf{B_{73}}$ | = | $\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+a z_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{74}}$ | = | $\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+a z_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{75}}$ | = | $\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}- a z_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{76}}$ | = | $- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}- a z_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{77}}$ | = | $\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{1}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $a z_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}+a y_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{78}}$ | = | $- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $a z_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- a y_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{79}}$ | = | $\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{2}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a z_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}+a y_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{80}}$ | = | $\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a z_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- a y_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{81}}$ | = | $\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{2}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}+a z_{18} \,\mathbf{\hat{y}}+a x_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{82}}$ | = | $\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}+a z_{18} \,\mathbf{\hat{y}}- a x_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{83}}$ | = | $- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(- x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}- a z_{18} \,\mathbf{\hat{y}}- a x_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{84}}$ | = | $\left(x_{18} + y_{18} - z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} - y_{18} + z_{18}\right) \, \mathbf{a}_{2}- \left(x_{18} + y_{18} + z_{18}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}- a z_{18} \,\mathbf{\hat{y}}+a x_{18} \,\mathbf{\hat{z}}$ | (48h) | Li XIV |
| $\mathbf{B_{85}}$ | = | $\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}+a z_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{86}}$ | = | $\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}+a z_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{87}}$ | = | $\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+a y_{19} \,\mathbf{\hat{y}}- a z_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{88}}$ | = | $- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}- a y_{19} \,\mathbf{\hat{y}}- a z_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{89}}$ | = | $\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{1}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $a z_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}+a y_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{90}}$ | = | $- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $a z_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}- a y_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{91}}$ | = | $\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{2}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a z_{19} \,\mathbf{\hat{x}}- a x_{19} \,\mathbf{\hat{y}}+a y_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{92}}$ | = | $\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a z_{19} \,\mathbf{\hat{x}}+a x_{19} \,\mathbf{\hat{y}}- a y_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{93}}$ | = | $\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{2}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $a y_{19} \,\mathbf{\hat{x}}+a z_{19} \,\mathbf{\hat{y}}+a x_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{94}}$ | = | $\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a y_{19} \,\mathbf{\hat{x}}+a z_{19} \,\mathbf{\hat{y}}- a x_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{95}}$ | = | $- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{1}+\left(- x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{2}+\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{3}$ | = | $a y_{19} \,\mathbf{\hat{x}}- a z_{19} \,\mathbf{\hat{y}}- a x_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{96}}$ | = | $\left(x_{19} + y_{19} - z_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19} + z_{19}\right) \, \mathbf{a}_{2}- \left(x_{19} + y_{19} + z_{19}\right) \, \mathbf{a}_{3}$ | = | $- a y_{19} \,\mathbf{\hat{x}}- a z_{19} \,\mathbf{\hat{y}}+a x_{19} \,\mathbf{\hat{z}}$ | (48h) | Li XV |
| $\mathbf{B_{97}}$ | = | $\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}+a z_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{98}}$ | = | $\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}+a z_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{99}}$ | = | $\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+a y_{20} \,\mathbf{\hat{y}}- a z_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{100}}$ | = | $- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}- a y_{20} \,\mathbf{\hat{y}}- a z_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{101}}$ | = | $\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{1}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $a z_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}+a y_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{102}}$ | = | $- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $a z_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}- a y_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{103}}$ | = | $\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{2}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a z_{20} \,\mathbf{\hat{x}}- a x_{20} \,\mathbf{\hat{y}}+a y_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{104}}$ | = | $\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a z_{20} \,\mathbf{\hat{x}}+a x_{20} \,\mathbf{\hat{y}}- a y_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{105}}$ | = | $\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{2}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $a y_{20} \,\mathbf{\hat{x}}+a z_{20} \,\mathbf{\hat{y}}+a x_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{106}}$ | = | $\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a y_{20} \,\mathbf{\hat{x}}+a z_{20} \,\mathbf{\hat{y}}- a x_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{107}}$ | = | $- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{1}+\left(- x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{2}+\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{3}$ | = | $a y_{20} \,\mathbf{\hat{x}}- a z_{20} \,\mathbf{\hat{y}}- a x_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
| $\mathbf{B_{108}}$ | = | $\left(x_{20} + y_{20} - z_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20} + z_{20}\right) \, \mathbf{a}_{2}- \left(x_{20} + y_{20} + z_{20}\right) \, \mathbf{a}_{3}$ | = | $- a y_{20} \,\mathbf{\hat{x}}- a z_{20} \,\mathbf{\hat{y}}+a x_{20} \,\mathbf{\hat{z}}$ | (48h) | Li XVI |
References
- H. Axel, H. Schäfer, and A. Weiss, Zur Kenntnis der Phase Li$_{22}$Si$_{5}$, Z. Naturforsch. B 21, 115–117 (1966), doi:10.1515/znb-1966-0204.
- A. Zalkin and W. J. Ramsey, Intermetallic compounds between lithium and lead. IV. The crystal structure of Li$_{22}$Pb$_{5}$, J. Physic. Chem. 62, 689–693 (1958), doi:10.1021/j150564a013.
- G. R. Goward, N. J. Taylor, D. C. S. Souza, and L. F. Nazar, The true crystal structure of Li$_{17}$M$_{4}$ (M=Ge, Sn, Pb)-revised from Li$_{22}$M$_{5}$, J. Alloys Compd. 329, 82–91 (2001), doi:10.1016/S0925-8388(01)01567-5.
Found in
- Inorganic Crystal Structure Database}. Entry 24596 (Li$_{22}$Si$_{5$).
Prototype Generator
aflow --proto=A22B5_cF432_196_abcd6efg4h_2efg --params=$a,x_{5},x_{6},x_{7},x_{8},x_{9},x_{10},x_{11},x_{12},x_{13},x_{14},x_{15},x_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20}$