Low Temperature Body-Centered Tetragonal CH$_{3}$NH$_{3}$PbBr$_{3}$ Structure: A3B8C48D8E_tI272_140_ah_m_6m_m_c-001
| Prototype | Br$_{3}$CH$_{6}$NPb |
| AFLOW prototype label | A3B8C48D8E_tI272_140_ah_m_6m_m_c-001 |
| Pearson symbol | tI272 |
| Space group number | 140 |
| Space group symbol | $I4/mcm$ |
| AFLOW prototype command |
aflow --proto=A3B8C48D8E_tI272_140_ah_m_6m_m_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
- CH$_{3}$NH$_{3}$PbBr$_{3}$ can be found in a variety of distorted perovskite ($E2_{1}$) structures, depending upon the temperature and pressure (Abia, 2022; Liang, 2023):
- A low temperature orthorhombic structure, stable below 145K.
- An intermediate temperature body-centered orthorhombic structure, stable from 145-157K.
- This intermediate temperature tetragonal structure, stable from 156-229K.
- The room-temperature cubic perovskite-like structure, stable above 229K.
- A cubic high-pressure Phase II structure, stable from 0.9-1.8 GPa.
- An orthorhombic Phase III structure, stable from 1.8-4.6 GPa.
- Another orthorhombic Phase IV structure was found by (Liang, 2023), but the atomic positions have yet to be calculated.
- We report the data taken at 155.6K.
- Only 1/8 of the carbon, nitrogen, and hydrogen (32m) sites are occupied, yielding one CH$_{3}$-NH$_{3}$ complex per unit cell.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Br I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4a) | Br I |
| $\mathbf{B_{3}}$ | = | $0$ | = | $0$ | (4c) | Pb I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4c) | Pb I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Br II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}$ | (8h) | Br II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}$ | (8h) | Br II |
| $\mathbf{B_{8}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}$ | (8h) | Br II |
| $\mathbf{B_{9}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{10}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{11}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{12}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{13}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{14}}$ | = | $- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{15}}$ | = | $\left(x_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{17}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{18}}$ | = | $\left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{19}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{20}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{21}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{22}}$ | = | $\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{23}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{24}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | C I |
| $\mathbf{B_{25}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{26}}$ | = | $- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{27}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{28}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{29}}$ | = | $\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{30}}$ | = | $- \left(y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{31}}$ | = | $\left(x_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{32}}$ | = | $- \left(x_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{33}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{34}}$ | = | $\left(y_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{35}}$ | = | $- \left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(y_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{36}}$ | = | $\left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{37}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{38}}$ | = | $\left(y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{39}}$ | = | $\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{40}}$ | = | $\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{5} + y_{5}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H I |
| $\mathbf{B_{41}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{42}}$ | = | $- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{43}}$ | = | $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{44}}$ | = | $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{45}}$ | = | $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{46}}$ | = | $- \left(y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{47}}$ | = | $\left(x_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{48}}$ | = | $- \left(x_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{49}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{50}}$ | = | $\left(y_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{51}}$ | = | $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{52}}$ | = | $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{53}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{54}}$ | = | $\left(y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{55}}$ | = | $\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{56}}$ | = | $\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H II |
| $\mathbf{B_{57}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{58}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{59}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{60}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{61}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{62}}$ | = | $- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{63}}$ | = | $\left(x_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{64}}$ | = | $- \left(x_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{65}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{66}}$ | = | $\left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{67}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{68}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{69}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{70}}$ | = | $\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{71}}$ | = | $\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{72}}$ | = | $\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H III |
| $\mathbf{B_{73}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{74}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{75}}$ | = | $\left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{76}}$ | = | $- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{77}}$ | = | $\left(y_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{78}}$ | = | $- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{79}}$ | = | $\left(x_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{80}}$ | = | $- \left(x_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{81}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{82}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{83}}$ | = | $- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{84}}$ | = | $\left(x_{8} - z_{8}\right) \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{85}}$ | = | $\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{86}}$ | = | $\left(y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{87}}$ | = | $\left(- x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{88}}$ | = | $\left(x_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{8} + z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{8} + y_{8}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H IV |
| $\mathbf{B_{89}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{90}}$ | = | $- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{91}}$ | = | $\left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{92}}$ | = | $- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{93}}$ | = | $\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{94}}$ | = | $- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{95}}$ | = | $\left(x_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{96}}$ | = | $- \left(x_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{97}}$ | = | $- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{98}}$ | = | $\left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{99}}$ | = | $- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{100}}$ | = | $\left(x_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{101}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{102}}$ | = | $\left(y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{103}}$ | = | $\left(- x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{104}}$ | = | $\left(x_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H V |
| $\mathbf{B_{105}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{106}}$ | = | $- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{107}}$ | = | $\left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{108}}$ | = | $- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{109}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{110}}$ | = | $- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{111}}$ | = | $\left(x_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{112}}$ | = | $- \left(x_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{113}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{114}}$ | = | $\left(y_{10} - z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{115}}$ | = | $- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(y_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{116}}$ | = | $\left(x_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{117}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{118}}$ | = | $\left(y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{119}}$ | = | $\left(- x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{120}}$ | = | $\left(x_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | H VI |
| $\mathbf{B_{121}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{122}}$ | = | $- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{123}}$ | = | $\left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{124}}$ | = | $- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{125}}$ | = | $\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{126}}$ | = | $- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{127}}$ | = | $\left(x_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{128}}$ | = | $- \left(x_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{129}}$ | = | $- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{130}}$ | = | $\left(y_{11} - z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{131}}$ | = | $- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(y_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{132}}$ | = | $\left(x_{11} - z_{11}\right) \, \mathbf{a}_{1}- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{133}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{134}}$ | = | $\left(y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{135}}$ | = | $\left(- x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
| $\mathbf{B_{136}}$ | = | $\left(x_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (32m) | N I |
References
- C. Abia, C. A. López, L. C. {n}adillas Delgado, M. T. Fernández-Diaz, and J. A. Alonso, Crystal structure thermal evolution and novel orthorhombic phase of methylammonium lead bromide, CH$_{3}$NH$_{3}$PbBr$_{3}$, Sci. Rep. 12, 18647 (2022), doi:10.1038/s41598-022-21544-2.
- A. Liang, R. Turnbull, C. Popescu, I. Fernandez-Guillen, R. Abargues, P. P. Boix, and D. Errandonea, Pressure-Induced Phase Transition versus Amorphization in Hybrid Methylammonium Lead Bromide Perovskite, J. Phys. Chem. C 127, 12821–12826 (2023), doi:10.1021/acs.jpcc.3c03263.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A3B8C48D8E_tI272_140_ah_m_6m_m_c --params=$a,c/a,x_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$