Er$_{5}$Rh$_{6}$Sn$_{18}$ Structure: A5B6C18_tI232_142_bg_dg_e2f3g-001
| Prototype | Er$_{5}$Rh$_{6}$Sn$_{18}$ |
| AFLOW prototype label | A5B6C18_tI232_142_bg_dg_e2f3g-001 |
| ICSD | 103302 |
| Pearson symbol | tI232 |
| Space group number | 142 |
| Space group symbol | $I4_1/acd$ |
| AFLOW prototype command |
aflow --proto=A5B6C18_tI232_142_bg_dg_e2f3g-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}$ |
Other compounds with this structure
Lu$_{5}$Rh$_{6}$Sn$_{18}$, Sc$_{5}$Rh$_{6}$Sn$_{18}$, Y$_{5}$Rh$_{6}$Sn$_{18}$
- (Hodeau, 1984) found that the Er-I site is actually a mixture of erbium and tin atoms in a 2:1 ratio. The ICSD entry assumes a 1:2 ratio.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8b) | Er I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (8b) | Er I |
| $\mathbf{B_{3}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8b) | Er I |
| $\mathbf{B_{4}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (8b) | Er I |
| $\mathbf{B_{5}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{6}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{7}}$ | = | $- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{8}}$ | = | $- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{9}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{10}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{11}}$ | = | $\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{12}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16d) | Rh I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{14}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{15}}$ | = | $\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}$ | (16e) | Sn I |
| $\mathbf{B_{17}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{18}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{20}}$ | = | $\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (16e) | Sn I |
| $\mathbf{B_{21}}$ | = | $\left(x_{4} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{22}}$ | = | $- \left(x_{4} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{23}}$ | = | $\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{24}}$ | = | $- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{25}}$ | = | $- \left(x_{4} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{26}}$ | = | $\left(x_{4} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{4} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{28}}$ | = | $\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{4} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn II |
| $\mathbf{B_{29}}$ | = | $\left(x_{5} + \frac{3}{8}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{5} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{30}}$ | = | $- \left(x_{5} - \frac{3}{8}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{5} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{31}}$ | = | $\left(x_{5} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{32}}$ | = | $- \left(x_{5} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{3}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{33}}$ | = | $- \left(x_{5} - \frac{5}{8}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{5} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{34}}$ | = | $\left(x_{5} + \frac{5}{8}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{5} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{35}}$ | = | $- \left(x_{5} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{5} + \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{36}}$ | = | $\left(x_{5} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{5} - \frac{5}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{5}{8}c \,\mathbf{\hat{z}}$ | (16f) | Sn III |
| $\mathbf{B_{37}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{38}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{39}}$ | = | $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{40}}$ | = | $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{41}}$ | = | $\left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{42}}$ | = | $- \left(y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{43}}$ | = | $\left(x_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{44}}$ | = | $- \left(x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{45}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{46}}$ | = | $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{47}}$ | = | $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{48}}$ | = | $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{49}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{50}}$ | = | $\left(y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{51}}$ | = | $\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{52}}$ | = | $\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Er II |
| $\mathbf{B_{53}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{54}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{55}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{56}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{57}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{58}}$ | = | $- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{59}}$ | = | $\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{60}}$ | = | $- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{61}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{62}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{63}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{64}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{65}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{66}}$ | = | $\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{67}}$ | = | $\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{7} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{68}}$ | = | $\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{7} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{7} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Rh II |
| $\mathbf{B_{69}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{70}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{71}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{72}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{73}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{74}}$ | = | $- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{75}}$ | = | $\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{76}}$ | = | $- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{77}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{78}}$ | = | $\left(y_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{79}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{80}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{81}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{82}}$ | = | $\left(y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{83}}$ | = | $\left(- x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{8} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{84}}$ | = | $\left(x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{8} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{8} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn IV |
| $\mathbf{B_{85}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{86}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{87}}$ | = | $\left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{88}}$ | = | $- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{89}}$ | = | $\left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{90}}$ | = | $- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{91}}$ | = | $\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{92}}$ | = | $- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{93}}$ | = | $- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{94}}$ | = | $\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{95}}$ | = | $- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{96}}$ | = | $\left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{97}}$ | = | $- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{98}}$ | = | $\left(y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{99}}$ | = | $\left(- x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{9} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{100}}$ | = | $\left(x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{9} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{9} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn V |
| $\mathbf{B_{101}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{102}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{103}}$ | = | $\left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{104}}$ | = | $- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{105}}$ | = | $\left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{106}}$ | = | $- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{107}}$ | = | $\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{108}}$ | = | $- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{109}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{110}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{111}}$ | = | $- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{112}}$ | = | $\left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{113}}$ | = | $- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{114}}$ | = | $\left(y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{115}}$ | = | $\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{10} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
| $\mathbf{B_{116}}$ | = | $\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{10} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{10} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (32g) | Sn VI |
References
- J. L. Hodeau, M. Marezio, and J. P. Remeika, The structure of [Er(1)$_{1-x}$,Sn(1)$_{x}$]Er(2)$_{4}$Rh$_{6}$Sn(2)$_{4}$Sn(3)$_{12}$Sn(4)$_{2}$, a ternary reentrant superconductor, Acta Crystallogr. Sect. B 40, 26–38 (1984), doi:10.1107/S0108768184001713.
Found in
- A. Ślebarski, P. Zajdel, M. M. Maśka, J. Deniszczyk, and M. Fijałkowski, Superconductivity of Y$_{5}$Rh$_{6}$Sn$_{18}$; Coexistence of the high temperature thermal lattice relaxation process and superconductivity, J. Alloys Compd. 819, 152959 (2020), doi:10.1016/j.jallcom.2019.152959.
Prototype Generator
aflow --proto=A5B6C18_tI232_142_bg_dg_e2f3g --params=$a,c/a,z_{2},x_{3},x_{4},x_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10}$