Ba$_{19}$Li$_{44}$ Structure: A19B44_tI252_122_ac4e_2d10e-001
| Prototype | Ba$_{19}$Li$_{44}$ |
| AFLOW prototype label | A19B44_tI252_122_ac4e_2d10e-001 |
| ICSD | 249574 |
| Pearson symbol | tI252 |
| Space group number | 122 |
| Space group symbol | $I\overline{4}2d$ |
| AFLOW prototype command |
aflow --proto=A19B44_tI252_122_ac4e_2d10e-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Ba I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba II |
| $\mathbf{B_{4}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Ba II |
| $\mathbf{B_{5}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Ba II |
| $\mathbf{B_{6}}$ | = | $\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Ba II |
| $\mathbf{B_{7}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li I |
| $\mathbf{B_{8}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li I |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li I |
| $\mathbf{B_{11}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li II |
| $\mathbf{B_{12}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li II |
| $\mathbf{B_{13}}$ | = | $- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li II |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Li II |
| $\mathbf{B_{15}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{16}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{17}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{18}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{19}}$ | = | $\left(y_{5} - z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{20}}$ | = | $- \left(y_{5} + z_{5} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{21}}$ | = | $\left(- x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{22}}$ | = | $\left(x_{5} + z_{5} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba III |
| $\mathbf{B_{23}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{24}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{25}}$ | = | $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{26}}$ | = | $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{27}}$ | = | $\left(y_{6} - z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{28}}$ | = | $- \left(y_{6} + z_{6} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{29}}$ | = | $\left(- x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{30}}$ | = | $\left(x_{6} + z_{6} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba IV |
| $\mathbf{B_{31}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{32}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{33}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{34}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{35}}$ | = | $\left(y_{7} - z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{36}}$ | = | $- \left(y_{7} + z_{7} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{37}}$ | = | $\left(- x_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{38}}$ | = | $\left(x_{7} + z_{7} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba V |
| $\mathbf{B_{39}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{40}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{41}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{42}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{43}}$ | = | $\left(y_{8} - z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{44}}$ | = | $- \left(y_{8} + z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{45}}$ | = | $\left(- x_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{46}}$ | = | $\left(x_{8} + z_{8} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Ba VI |
| $\mathbf{B_{47}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{48}}$ | = | $- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{49}}$ | = | $- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{50}}$ | = | $\left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{51}}$ | = | $\left(y_{9} - z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{52}}$ | = | $- \left(y_{9} + z_{9} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{53}}$ | = | $\left(- x_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{54}}$ | = | $\left(x_{9} + z_{9} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li III |
| $\mathbf{B_{55}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{56}}$ | = | $- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{57}}$ | = | $- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{58}}$ | = | $\left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{59}}$ | = | $\left(y_{10} - z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{60}}$ | = | $- \left(y_{10} + z_{10} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{61}}$ | = | $\left(- x_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{62}}$ | = | $\left(x_{10} + z_{10} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IV |
| $\mathbf{B_{63}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{64}}$ | = | $- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{65}}$ | = | $- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{66}}$ | = | $\left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{67}}$ | = | $\left(y_{11} - z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{68}}$ | = | $- \left(y_{11} + z_{11} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{69}}$ | = | $\left(- x_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{70}}$ | = | $\left(x_{11} + z_{11} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li V |
| $\mathbf{B_{71}}$ | = | $\left(y_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(x_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{72}}$ | = | $- \left(y_{12} - z_{12}\right) \, \mathbf{a}_{1}- \left(x_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{73}}$ | = | $- \left(x_{12} + z_{12}\right) \, \mathbf{a}_{1}+\left(y_{12} - z_{12}\right) \, \mathbf{a}_{2}- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{74}}$ | = | $\left(x_{12} - z_{12}\right) \, \mathbf{a}_{1}- \left(y_{12} + z_{12}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{75}}$ | = | $\left(y_{12} - z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{12} + z_{12} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{12} + y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+a \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{76}}$ | = | $- \left(y_{12} + z_{12} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{12} - z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{12} - y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}- a \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{77}}$ | = | $\left(- x_{12} + z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{12} + y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{78}}$ | = | $\left(x_{12} + z_{12} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{12} + z_{12} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{12} + y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}+a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VI |
| $\mathbf{B_{79}}$ | = | $\left(y_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(x_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{80}}$ | = | $- \left(y_{13} - z_{13}\right) \, \mathbf{a}_{1}- \left(x_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{81}}$ | = | $- \left(x_{13} + z_{13}\right) \, \mathbf{a}_{1}+\left(y_{13} - z_{13}\right) \, \mathbf{a}_{2}- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{82}}$ | = | $\left(x_{13} - z_{13}\right) \, \mathbf{a}_{1}- \left(y_{13} + z_{13}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{83}}$ | = | $\left(y_{13} - z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{13} + z_{13} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{13} + y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+a \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{84}}$ | = | $- \left(y_{13} + z_{13} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{13} - z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{13} - y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}- a \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{85}}$ | = | $\left(- x_{13} + z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{13} + y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{86}}$ | = | $\left(x_{13} + z_{13} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{13} + z_{13} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{13} + y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}+a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VII |
| $\mathbf{B_{87}}$ | = | $\left(y_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(x_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{88}}$ | = | $- \left(y_{14} - z_{14}\right) \, \mathbf{a}_{1}- \left(x_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{89}}$ | = | $- \left(x_{14} + z_{14}\right) \, \mathbf{a}_{1}+\left(y_{14} - z_{14}\right) \, \mathbf{a}_{2}- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{90}}$ | = | $\left(x_{14} - z_{14}\right) \, \mathbf{a}_{1}- \left(y_{14} + z_{14}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{91}}$ | = | $\left(y_{14} - z_{14} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{14} + z_{14} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{14} + y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+a \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{92}}$ | = | $- \left(y_{14} + z_{14} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{14} - z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{14} - y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}- a \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{93}}$ | = | $\left(- x_{14} + z_{14} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{14} + y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{94}}$ | = | $\left(x_{14} + z_{14} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{14} + z_{14} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{14} + y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}+a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li VIII |
| $\mathbf{B_{95}}$ | = | $\left(y_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(x_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{96}}$ | = | $- \left(y_{15} - z_{15}\right) \, \mathbf{a}_{1}- \left(x_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{97}}$ | = | $- \left(x_{15} + z_{15}\right) \, \mathbf{a}_{1}+\left(y_{15} - z_{15}\right) \, \mathbf{a}_{2}- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{98}}$ | = | $\left(x_{15} - z_{15}\right) \, \mathbf{a}_{1}- \left(y_{15} + z_{15}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{99}}$ | = | $\left(y_{15} - z_{15} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{15} + z_{15} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{15} + y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+a \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{100}}$ | = | $- \left(y_{15} + z_{15} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{15} - z_{15} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{15} - y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}- a \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{101}}$ | = | $\left(- x_{15} + z_{15} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{15} + z_{15} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{15} + y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{102}}$ | = | $\left(x_{15} + z_{15} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{15} + z_{15} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{15} + y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}+a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li IX |
| $\mathbf{B_{103}}$ | = | $\left(y_{16} + z_{16}\right) \, \mathbf{a}_{1}+\left(x_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} + y_{16}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{104}}$ | = | $- \left(y_{16} - z_{16}\right) \, \mathbf{a}_{1}- \left(x_{16} - z_{16}\right) \, \mathbf{a}_{2}- \left(x_{16} + y_{16}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{105}}$ | = | $- \left(x_{16} + z_{16}\right) \, \mathbf{a}_{1}+\left(y_{16} - z_{16}\right) \, \mathbf{a}_{2}- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{106}}$ | = | $\left(x_{16} - z_{16}\right) \, \mathbf{a}_{1}- \left(y_{16} + z_{16}\right) \, \mathbf{a}_{2}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{107}}$ | = | $\left(y_{16} - z_{16} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{16} + z_{16} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{16} + y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+a \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{108}}$ | = | $- \left(y_{16} + z_{16} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{16} - z_{16} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{16} - y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}- a \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{109}}$ | = | $\left(- x_{16} + z_{16} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{16} + z_{16} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{16} + y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{110}}$ | = | $\left(x_{16} + z_{16} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{16} + z_{16} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{16} + y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}+a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li X |
| $\mathbf{B_{111}}$ | = | $\left(y_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{112}}$ | = | $- \left(y_{17} - z_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{113}}$ | = | $- \left(x_{17} + z_{17}\right) \, \mathbf{a}_{1}+\left(y_{17} - z_{17}\right) \, \mathbf{a}_{2}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{114}}$ | = | $\left(x_{17} - z_{17}\right) \, \mathbf{a}_{1}- \left(y_{17} + z_{17}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{115}}$ | = | $\left(y_{17} - z_{17} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{17} + z_{17} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{17} + y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+a \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{116}}$ | = | $- \left(y_{17} + z_{17} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{17} - z_{17} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{17} - y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- a \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{117}}$ | = | $\left(- x_{17} + z_{17} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{17} + z_{17} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{17} + y_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}- a \left(x_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{118}}$ | = | $\left(x_{17} + z_{17} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{17} + z_{17} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{17} + y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}+a \left(x_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XI |
| $\mathbf{B_{119}}$ | = | $\left(y_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} + y_{18}\right) \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{120}}$ | = | $- \left(y_{18} - z_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} - z_{18}\right) \, \mathbf{a}_{2}- \left(x_{18} + y_{18}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}- a y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{121}}$ | = | $- \left(x_{18} + z_{18}\right) \, \mathbf{a}_{1}+\left(y_{18} - z_{18}\right) \, \mathbf{a}_{2}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}- a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{122}}$ | = | $\left(x_{18} - z_{18}\right) \, \mathbf{a}_{1}- \left(y_{18} + z_{18}\right) \, \mathbf{a}_{2}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}+a x_{18} \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{123}}$ | = | $\left(y_{18} - z_{18} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{18} + z_{18} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(- x_{18} + y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+a \left(y_{18} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{124}}$ | = | $- \left(y_{18} + z_{18} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{18} - z_{18} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{18} - y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}- a \left(y_{18} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{125}}$ | = | $\left(- x_{18} + z_{18} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(- y_{18} + z_{18} + \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{18} + y_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{18} \,\mathbf{\hat{x}}- a \left(x_{18} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XII |
| $\mathbf{B_{126}}$ | = | $\left(x_{18} + z_{18} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{18} + z_{18} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\left(x_{18} + y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{18} \,\mathbf{\hat{x}}+a \left(x_{18} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16e) | Li XII |
References
- V. Smetana, V. Babizhetskyy, G. V. Vajenine, C. Hoch, and A. Simon, Double-Icosahedral Li Clusters in a New Binary Compound Ba$_{19}$Li$_{44}$: A Reinvestigation of the Ba−Li Phase Diagram, Inorg. Chem. 46, 5425–5428 (2007), doi:10.1021/ic070249i.
Found in
- H. Okamoto, Ba-Li (Barium-Lithium), J. Phase Equilibria Diffus. 31, 489 (2010), doi:10.1007/s11669-010-9755-z.
Prototype Generator
aflow --proto=A19B44_tI252_122_ac4e_2d10e --params=$a,c/a,z_{2},x_{3},x_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18}$