fcc Fullerene (K$_{3}$C$_{60}$) Structure: A40B_cF492_225_j2l_ac-001
| Prototype | C$_{60}$K$_{3}$ |
| AFLOW prototype label | A40B_cF492_225_j2l_ac-001 |
| ICSD | 66728 |
| Pearson symbol | cF492 |
| Space group number | 225 |
| Space group symbol | $Fm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A40B_cF492_225_j2l_ac-001
--params=$a, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}$ |
Other compounds with this structure
Cs$_{3}$C$_{60}$, CsK$_{2}$C$_{60}$, CsNa$_{2}$C$_{60}$, CsRb$_{2}$C$_{60}$, KNa$_{2}$C$_{60}$, Rb$_{3}$C$_{60}$, RbCs$_{2}$C$_{60}$, RbNa$_{2}$C$_{60}$
- All of the carbon sites are occupied only 50% of the time.
- (Stephens, 1991) put the K-I atom on the (4b) Wyckoff position, $(1/2,1/2,1/2)$. We shifted this so that the atom is at the origin, the (4a) Wyckoff site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | K I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (8c) | K II |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (8c) | K II |
| $\mathbf{B_{4}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{5}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{6}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{7}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{8}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{10}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{12}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{13}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{14}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{15}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{16}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{19}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{20}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{21}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{23}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96j) | C I |
| $\mathbf{B_{24}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{25}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{26}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{27}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}$ | (96j) | C I |
| $\mathbf{B_{28}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{29}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{30}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{31}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{32}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{34}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{35}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{36}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{37}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{38}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{39}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{40}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{41}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{42}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{43}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{44}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{45}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{46}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{47}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{48}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{49}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{50}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{51}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{52}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{53}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{54}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{55}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{56}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{57}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{58}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{59}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{60}}$ | = | $- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{61}}$ | = | $\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{62}}$ | = | $\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{63}}$ | = | $- \left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{64}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{65}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{66}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{67}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- a z_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{68}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{69}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a z_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{70}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}+a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{71}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a z_{4} \,\mathbf{\hat{y}}- a y_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{72}}$ | = | $\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{73}}$ | = | $\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{3}$ | = | $- a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{74}}$ | = | $- \left(x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{75}}$ | = | $\left(x_{4} + y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(- x_{4} + y_{4} + z_{4}\right) \, \mathbf{a}_{3}$ | = | $a z_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+a x_{4} \,\mathbf{\hat{z}}$ | (192l) | C II |
| $\mathbf{B_{76}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{77}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{78}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{79}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{80}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{81}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{82}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{83}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{84}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{85}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{86}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{87}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{88}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{89}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{90}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{91}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{92}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{93}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{94}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{95}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{96}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{97}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{98}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{99}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{100}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{101}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{102}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{103}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{104}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{105}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{106}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{107}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{108}}$ | = | $- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{109}}$ | = | $\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{110}}$ | = | $\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{111}}$ | = | $- \left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{112}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{113}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{114}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{115}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- a z_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{116}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{117}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a z_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{118}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}+a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{119}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a z_{5} \,\mathbf{\hat{y}}- a y_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{120}}$ | = | $\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{121}}$ | = | $\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{3}$ | = | $- a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{122}}$ | = | $- \left(x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
| $\mathbf{B_{123}}$ | = | $\left(x_{5} + y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(- x_{5} + y_{5} + z_{5}\right) \, \mathbf{a}_{3}$ | = | $a z_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+a x_{5} \,\mathbf{\hat{z}}$ | (192l) | C III |
References
- P. W. Stephens, L. Mihaly, P. L. Lee, R. L. Whetten, S.-M. Huang, R. Kaner, F. Deiderich, and K. Holczer, Structure of single-phase superconducting K$_{3}$C$_{60}$, Nature 351, 632–634 (1991), doi:10.1038/351632a0.
Found in
- A. R. Kortan, N. Kopylov, R. M. Fleming, O. Zhou, F. A. Thiel, R. C. Haddon, and K. M. Rabe, Novel A15 phase in barium-doped fullerite, Phys. Rev. B 47, 13070–13074 (R) (1993), doi:10.1103/PhysRevB.47.13070.
Prototype Generator
aflow --proto=A40B_cF492_225_j2l_ac --params=$a,y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5}$