La$_{43}$Ni$_{17}$Mg$_{5}$ Structure: A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h-001
| Prototype | La$_{43}$Mg$_{5}$Ni$_{17}$ |
| AFLOW prototype label | A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h-001 |
| ICSD | 249963 |
| Pearson symbol | oC260 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}$ |
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $- y_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | La I |
| $\mathbf{B_{2}}$ | = | $y_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | La I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mg I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Mg I |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Ni I |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Ni I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (8e) | Ni II |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8e) | Ni II |
| $\mathbf{B_{9}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (8e) | Ni II |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (8e) | Ni II |
| $\mathbf{B_{11}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8f) | La II |
| $\mathbf{B_{12}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La II |
| $\mathbf{B_{13}}$ | = | $- y_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La II |
| $\mathbf{B_{14}}$ | = | $y_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8f) | La II |
| $\mathbf{B_{15}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8f) | La III |
| $\mathbf{B_{16}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La III |
| $\mathbf{B_{17}}$ | = | $- y_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La III |
| $\mathbf{B_{18}}$ | = | $y_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8f) | La III |
| $\mathbf{B_{19}}$ | = | $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8f) | La IV |
| $\mathbf{B_{20}}$ | = | $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La IV |
| $\mathbf{B_{21}}$ | = | $- y_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La IV |
| $\mathbf{B_{22}}$ | = | $y_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8f) | La IV |
| $\mathbf{B_{23}}$ | = | $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8f) | La V |
| $\mathbf{B_{24}}$ | = | $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La V |
| $\mathbf{B_{25}}$ | = | $- y_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La V |
| $\mathbf{B_{26}}$ | = | $y_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- b y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8f) | La V |
| $\mathbf{B_{27}}$ | = | $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (8f) | La VI |
| $\mathbf{B_{28}}$ | = | $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VI |
| $\mathbf{B_{29}}$ | = | $- y_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VI |
| $\mathbf{B_{30}}$ | = | $y_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (8f) | La VI |
| $\mathbf{B_{31}}$ | = | $- y_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (8f) | La VII |
| $\mathbf{B_{32}}$ | = | $y_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VII |
| $\mathbf{B_{33}}$ | = | $- y_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VII |
| $\mathbf{B_{34}}$ | = | $y_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (8f) | La VII |
| $\mathbf{B_{35}}$ | = | $- y_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (8f) | La VIII |
| $\mathbf{B_{36}}$ | = | $y_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VIII |
| $\mathbf{B_{37}}$ | = | $- y_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La VIII |
| $\mathbf{B_{38}}$ | = | $y_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (8f) | La VIII |
| $\mathbf{B_{39}}$ | = | $- y_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (8f) | La IX |
| $\mathbf{B_{40}}$ | = | $y_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La IX |
| $\mathbf{B_{41}}$ | = | $- y_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{12} \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La IX |
| $\mathbf{B_{42}}$ | = | $y_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- b y_{12} \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (8f) | La IX |
| $\mathbf{B_{43}}$ | = | $- y_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (8f) | Mg II |
| $\mathbf{B_{44}}$ | = | $y_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Mg II |
| $\mathbf{B_{45}}$ | = | $- y_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{13} \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Mg II |
| $\mathbf{B_{46}}$ | = | $y_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- b y_{13} \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (8f) | Mg II |
| $\mathbf{B_{47}}$ | = | $- y_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (8f) | Ni III |
| $\mathbf{B_{48}}$ | = | $y_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni III |
| $\mathbf{B_{49}}$ | = | $- y_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{14} \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni III |
| $\mathbf{B_{50}}$ | = | $y_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- b y_{14} \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (8f) | Ni III |
| $\mathbf{B_{51}}$ | = | $- y_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (8f) | Ni IV |
| $\mathbf{B_{52}}$ | = | $y_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni IV |
| $\mathbf{B_{53}}$ | = | $- y_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{15} \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni IV |
| $\mathbf{B_{54}}$ | = | $y_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- b y_{15} \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (8f) | Ni IV |
| $\mathbf{B_{55}}$ | = | $- y_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (8f) | Ni V |
| $\mathbf{B_{56}}$ | = | $y_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni V |
| $\mathbf{B_{57}}$ | = | $- y_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{16} \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Ni V |
| $\mathbf{B_{58}}$ | = | $y_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- b y_{16} \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (8f) | Ni V |
| $\mathbf{B_{59}}$ | = | $\left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} + y_{17}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | La X |
| $\mathbf{B_{60}}$ | = | $- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | La X |
| $\mathbf{B_{61}}$ | = | $- \left(x_{17} + y_{17}\right) \, \mathbf{a}_{1}- \left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | La X |
| $\mathbf{B_{62}}$ | = | $\left(x_{17} + y_{17}\right) \, \mathbf{a}_{1}+\left(x_{17} - y_{17}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | La X |
| $\mathbf{B_{63}}$ | = | $\left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} + y_{18}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Mg III |
| $\mathbf{B_{64}}$ | = | $- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} + y_{18}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Mg III |
| $\mathbf{B_{65}}$ | = | $- \left(x_{18} + y_{18}\right) \, \mathbf{a}_{1}- \left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Mg III |
| $\mathbf{B_{66}}$ | = | $\left(x_{18} + y_{18}\right) \, \mathbf{a}_{1}+\left(x_{18} - y_{18}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8g) | Mg III |
| $\mathbf{B_{67}}$ | = | $\left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{68}}$ | = | $- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{69}}$ | = | $- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{70}}$ | = | $\left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{71}}$ | = | $- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{72}}$ | = | $\left(x_{19} - y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} + y_{19}\right) \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{73}}$ | = | $\left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}+\left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{74}}$ | = | $- \left(x_{19} + y_{19}\right) \, \mathbf{a}_{1}- \left(x_{19} - y_{19}\right) \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (16h) | La XI |
| $\mathbf{B_{75}}$ | = | $\left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{76}}$ | = | $- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{77}}$ | = | $- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{78}}$ | = | $\left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{79}}$ | = | $- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{80}}$ | = | $\left(x_{20} - y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} + y_{20}\right) \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{81}}$ | = | $\left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}+\left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{82}}$ | = | $- \left(x_{20} + y_{20}\right) \, \mathbf{a}_{1}- \left(x_{20} - y_{20}\right) \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (16h) | La XII |
| $\mathbf{B_{83}}$ | = | $\left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}+\left(x_{21} + y_{21}\right) \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{84}}$ | = | $- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}- \left(x_{21} + y_{21}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{85}}$ | = | $- \left(x_{21} + y_{21}\right) \, \mathbf{a}_{1}- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{86}}$ | = | $\left(x_{21} + y_{21}\right) \, \mathbf{a}_{1}+\left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{87}}$ | = | $- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}- \left(x_{21} + y_{21}\right) \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{88}}$ | = | $\left(x_{21} - y_{21}\right) \, \mathbf{a}_{1}+\left(x_{21} + y_{21}\right) \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{89}}$ | = | $\left(x_{21} + y_{21}\right) \, \mathbf{a}_{1}+\left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{90}}$ | = | $- \left(x_{21} + y_{21}\right) \, \mathbf{a}_{1}- \left(x_{21} - y_{21}\right) \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (16h) | La XIII |
| $\mathbf{B_{91}}$ | = | $\left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}+\left(x_{22} + y_{22}\right) \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{92}}$ | = | $- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}- \left(x_{22} + y_{22}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{93}}$ | = | $- \left(x_{22} + y_{22}\right) \, \mathbf{a}_{1}- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{94}}$ | = | $\left(x_{22} + y_{22}\right) \, \mathbf{a}_{1}+\left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{95}}$ | = | $- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}- \left(x_{22} + y_{22}\right) \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{96}}$ | = | $\left(x_{22} - y_{22}\right) \, \mathbf{a}_{1}+\left(x_{22} + y_{22}\right) \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{97}}$ | = | $\left(x_{22} + y_{22}\right) \, \mathbf{a}_{1}+\left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{98}}$ | = | $- \left(x_{22} + y_{22}\right) \, \mathbf{a}_{1}- \left(x_{22} - y_{22}\right) \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (16h) | La XIV |
| $\mathbf{B_{99}}$ | = | $\left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}+\left(x_{23} + y_{23}\right) \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{100}}$ | = | $- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}- \left(x_{23} + y_{23}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{101}}$ | = | $- \left(x_{23} + y_{23}\right) \, \mathbf{a}_{1}- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}- \left(z_{23} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{102}}$ | = | $\left(x_{23} + y_{23}\right) \, \mathbf{a}_{1}+\left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{103}}$ | = | $- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}- \left(x_{23} + y_{23}\right) \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{104}}$ | = | $\left(x_{23} - y_{23}\right) \, \mathbf{a}_{1}+\left(x_{23} + y_{23}\right) \, \mathbf{a}_{2}- \left(z_{23} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{105}}$ | = | $\left(x_{23} + y_{23}\right) \, \mathbf{a}_{1}+\left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{106}}$ | = | $- \left(x_{23} + y_{23}\right) \, \mathbf{a}_{1}- \left(x_{23} - y_{23}\right) \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (16h) | La XV |
| $\mathbf{B_{107}}$ | = | $\left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}+\left(x_{24} + y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{108}}$ | = | $- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}- \left(x_{24} + y_{24}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{109}}$ | = | $- \left(x_{24} + y_{24}\right) \, \mathbf{a}_{1}- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}- \left(z_{24} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{110}}$ | = | $\left(x_{24} + y_{24}\right) \, \mathbf{a}_{1}+\left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{111}}$ | = | $- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}- \left(x_{24} + y_{24}\right) \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{112}}$ | = | $\left(x_{24} - y_{24}\right) \, \mathbf{a}_{1}+\left(x_{24} + y_{24}\right) \, \mathbf{a}_{2}- \left(z_{24} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{113}}$ | = | $\left(x_{24} + y_{24}\right) \, \mathbf{a}_{1}+\left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{114}}$ | = | $- \left(x_{24} + y_{24}\right) \, \mathbf{a}_{1}- \left(x_{24} - y_{24}\right) \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (16h) | La XVI |
| $\mathbf{B_{115}}$ | = | $\left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}+\left(x_{25} + y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{116}}$ | = | $- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}- \left(x_{25} + y_{25}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{117}}$ | = | $- \left(x_{25} + y_{25}\right) \, \mathbf{a}_{1}- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}- \left(z_{25} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}- c \left(z_{25} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{118}}$ | = | $\left(x_{25} + y_{25}\right) \, \mathbf{a}_{1}+\left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}- c z_{25} \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{119}}$ | = | $- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}- \left(x_{25} + y_{25}\right) \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}- c z_{25} \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{120}}$ | = | $\left(x_{25} - y_{25}\right) \, \mathbf{a}_{1}+\left(x_{25} + y_{25}\right) \, \mathbf{a}_{2}- \left(z_{25} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}- c \left(z_{25} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{121}}$ | = | $\left(x_{25} + y_{25}\right) \, \mathbf{a}_{1}+\left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{25} \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{122}}$ | = | $- \left(x_{25} + y_{25}\right) \, \mathbf{a}_{1}- \left(x_{25} - y_{25}\right) \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $- a x_{25} \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ | (16h) | Ni VI |
| $\mathbf{B_{123}}$ | = | $\left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} + y_{26}\right) \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{124}}$ | = | $- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}- \left(x_{26} + y_{26}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{125}}$ | = | $- \left(x_{26} + y_{26}\right) \, \mathbf{a}_{1}- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}- \left(z_{26} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}- c \left(z_{26} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{126}}$ | = | $\left(x_{26} + y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}- z_{26} \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}- c z_{26} \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{127}}$ | = | $- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}- \left(x_{26} + y_{26}\right) \, \mathbf{a}_{2}- z_{26} \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}- c z_{26} \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{128}}$ | = | $\left(x_{26} - y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} + y_{26}\right) \, \mathbf{a}_{2}- \left(z_{26} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}- c \left(z_{26} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{129}}$ | = | $\left(x_{26} + y_{26}\right) \, \mathbf{a}_{1}+\left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{26} \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
| $\mathbf{B_{130}}$ | = | $- \left(x_{26} + y_{26}\right) \, \mathbf{a}_{1}- \left(x_{26} - y_{26}\right) \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $- a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ | (16h) | Ni VII |
References
- P. Solokha, S. D. Negri, V. Pavlyuk, and A. Saccone, Anti-Mackay Polyicosahedral Clusters in La-Ni-Mg Ternary Compounds: Synthesis and Crystal Structure of the La$_{43}$Ni$_{17}$Mg$_{5}$ New Intermetallic Phase, Inorg. Chem. 48, 11586–11593 (2009), doi:10.1021/ic901422v.
Prototype Generator
aflow --proto=A43B5C17_oC260_63_c8fg6h_cfg_ce3f2h --params=$a,b/a,c/a,y_{1},y_{2},y_{3},x_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},y_{8},z_{8},y_{9},z_{9},y_{10},z_{10},y_{11},z_{11},y_{12},z_{12},y_{13},z_{13},y_{14},z_{14},y_{15},z_{15},y_{16},z_{16},x_{17},y_{17},x_{18},y_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26}$