Pb$_{3}$TeCo$_{3}$P$_{2}$O$_{14}$ Structure: A3B14C2D3E_mP138_3_3c3d6e_42e_6e_3a3b6e_3a3b-001
| Prototype | Co$_{3}$O$_{14}$P$_{2}$Pb$_{3}$Te |
| AFLOW prototype label | A3B14C2D3E_mP138_3_3c3d6e_42e_6e_3a3b6e_3a3b-001 |
| ICSD | 425850 |
| Pearson symbol | mP138 |
| Space group number | 3 |
| Space group symbol | $P2$ |
| AFLOW prototype command |
aflow --proto=A3B14C2D3E_mP138_3_3c3d6e_42e_6e_3a3b6e_3a3b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \beta, \allowbreak y_{1}, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak y_{6}, \allowbreak y_{7}, \allowbreak y_{8}, \allowbreak y_{9}, \allowbreak y_{10}, \allowbreak y_{11}, \allowbreak y_{12}, \allowbreak y_{13}, \allowbreak y_{14}, \allowbreak y_{15}, \allowbreak y_{16}, \allowbreak y_{17}, \allowbreak y_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}, \allowbreak x_{25}, \allowbreak y_{25}, \allowbreak z_{25}, \allowbreak x_{26}, \allowbreak y_{26}, \allowbreak z_{26}, \allowbreak x_{27}, \allowbreak y_{27}, \allowbreak z_{27}, \allowbreak x_{28}, \allowbreak y_{28}, \allowbreak z_{28}, \allowbreak x_{29}, \allowbreak y_{29}, \allowbreak z_{29}, \allowbreak x_{30}, \allowbreak y_{30}, \allowbreak z_{30}, \allowbreak x_{31}, \allowbreak y_{31}, \allowbreak z_{31}, \allowbreak x_{32}, \allowbreak y_{32}, \allowbreak z_{32}, \allowbreak x_{33}, \allowbreak y_{33}, \allowbreak z_{33}, \allowbreak x_{34}, \allowbreak y_{34}, \allowbreak z_{34}, \allowbreak x_{35}, \allowbreak y_{35}, \allowbreak z_{35}, \allowbreak x_{36}, \allowbreak y_{36}, \allowbreak z_{36}, \allowbreak x_{37}, \allowbreak y_{37}, \allowbreak z_{37}, \allowbreak x_{38}, \allowbreak y_{38}, \allowbreak z_{38}, \allowbreak x_{39}, \allowbreak y_{39}, \allowbreak z_{39}, \allowbreak x_{40}, \allowbreak y_{40}, \allowbreak z_{40}, \allowbreak x_{41}, \allowbreak y_{41}, \allowbreak z_{41}, \allowbreak x_{42}, \allowbreak y_{42}, \allowbreak z_{42}, \allowbreak x_{43}, \allowbreak y_{43}, \allowbreak z_{43}, \allowbreak x_{44}, \allowbreak y_{44}, \allowbreak z_{44}, \allowbreak x_{45}, \allowbreak y_{45}, \allowbreak z_{45}, \allowbreak x_{46}, \allowbreak y_{46}, \allowbreak z_{46}, \allowbreak x_{47}, \allowbreak y_{47}, \allowbreak z_{47}, \allowbreak x_{48}, \allowbreak y_{48}, \allowbreak z_{48}, \allowbreak x_{49}, \allowbreak y_{49}, \allowbreak z_{49}, \allowbreak x_{50}, \allowbreak y_{50}, \allowbreak z_{50}, \allowbreak x_{51}, \allowbreak y_{51}, \allowbreak z_{51}, \allowbreak x_{52}, \allowbreak y_{52}, \allowbreak z_{52}, \allowbreak x_{53}, \allowbreak y_{53}, \allowbreak z_{53}, \allowbreak x_{54}, \allowbreak y_{54}, \allowbreak z_{54}, \allowbreak x_{55}, \allowbreak y_{55}, \allowbreak z_{55}, \allowbreak x_{56}, \allowbreak y_{56}, \allowbreak z_{56}, \allowbreak x_{57}, \allowbreak y_{57}, \allowbreak z_{57}, \allowbreak x_{58}, \allowbreak y_{58}, \allowbreak z_{58}, \allowbreak x_{59}, \allowbreak y_{59}, \allowbreak z_{59}, \allowbreak x_{60}, \allowbreak y_{60}, \allowbreak z_{60}, \allowbreak x_{61}, \allowbreak y_{61}, \allowbreak z_{61}, \allowbreak x_{62}, \allowbreak y_{62}, \allowbreak z_{62}, \allowbreak x_{63}, \allowbreak y_{63}, \allowbreak z_{63}, \allowbreak x_{64}, \allowbreak y_{64}, \allowbreak z_{64}, \allowbreak x_{65}, \allowbreak y_{65}, \allowbreak z_{65}, \allowbreak x_{66}, \allowbreak y_{66}, \allowbreak z_{66}, \allowbreak x_{67}, \allowbreak y_{67}, \allowbreak z_{67}, \allowbreak x_{68}, \allowbreak y_{68}, \allowbreak z_{68}, \allowbreak x_{69}, \allowbreak y_{69}, \allowbreak z_{69}, \allowbreak x_{70}, \allowbreak y_{70}, \allowbreak z_{70}, \allowbreak x_{71}, \allowbreak y_{71}, \allowbreak z_{71}, \allowbreak x_{72}, \allowbreak y_{72}, \allowbreak z_{72}, \allowbreak x_{73}, \allowbreak y_{73}, \allowbreak z_{73}, \allowbreak x_{74}, \allowbreak y_{74}, \allowbreak z_{74}, \allowbreak x_{75}, \allowbreak y_{75}, \allowbreak z_{75}, \allowbreak x_{76}, \allowbreak y_{76}, \allowbreak z_{76}, \allowbreak x_{77}, \allowbreak y_{77}, \allowbreak z_{77}, \allowbreak x_{78}, \allowbreak y_{78}, \allowbreak z_{78}$ |
Other compounds with this structure
Pb$_{3}$TeCo$_{3}$V$_{2}$O$_{14}$
- This is a derivative of the dugganite/langasite structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \cos{\beta} \,\mathbf{\hat{x}}+c \sin{\beta} \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $y_{1} \, \mathbf{a}_{2}$ | = | $b y_{1} \,\mathbf{\hat{y}}$ | (1a) | Pb I |
| $\mathbf{B_{2}}$ | = | $y_{2} \, \mathbf{a}_{2}$ | = | $b y_{2} \,\mathbf{\hat{y}}$ | (1a) | Pb II |
| $\mathbf{B_{3}}$ | = | $y_{3} \, \mathbf{a}_{2}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (1a) | Pb III |
| $\mathbf{B_{4}}$ | = | $y_{4} \, \mathbf{a}_{2}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (1a) | Te I |
| $\mathbf{B_{5}}$ | = | $y_{5} \, \mathbf{a}_{2}$ | = | $b y_{5} \,\mathbf{\hat{y}}$ | (1a) | Te II |
| $\mathbf{B_{6}}$ | = | $y_{6} \, \mathbf{a}_{2}$ | = | $b y_{6} \,\mathbf{\hat{y}}$ | (1a) | Te III |
| $\mathbf{B_{7}}$ | = | $y_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Pb IV |
| $\mathbf{B_{8}}$ | = | $y_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Pb V |
| $\mathbf{B_{9}}$ | = | $y_{9} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Pb VI |
| $\mathbf{B_{10}}$ | = | $y_{10} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Te IV |
| $\mathbf{B_{11}}$ | = | $y_{11} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Te V |
| $\mathbf{B_{12}}$ | = | $y_{12} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \cos{\beta} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1b) | Te VI |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}$ | (1c) | Co I |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}$ | (1c) | Co II |
| $\mathbf{B_{15}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}$ | (1c) | Co III |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}\left(a + c \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1d) | Co IV |
| $\mathbf{B_{17}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}\left(a + c \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1d) | Co V |
| $\mathbf{B_{18}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}\left(a + c \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+\frac{1}{2}c \sin{\beta} \,\mathbf{\hat{z}}$ | (1d) | Co VI |
| $\mathbf{B_{19}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co VII |
| $\mathbf{B_{20}}$ | = | $- x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- \left(a x_{19} + c z_{19} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}- c z_{19} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co VII |
| $\mathbf{B_{21}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co VIII |
| $\mathbf{B_{22}}$ | = | $- x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- \left(a x_{20} + c z_{20} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}- c z_{20} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co VIII |
| $\mathbf{B_{23}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co IX |
| $\mathbf{B_{24}}$ | = | $- x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $- \left(a x_{21} + c z_{21} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}- c z_{21} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co IX |
| $\mathbf{B_{25}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + c z_{22} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co X |
| $\mathbf{B_{26}}$ | = | $- x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $- \left(a x_{22} + c z_{22} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}- c z_{22} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co X |
| $\mathbf{B_{27}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + c z_{23} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co XI |
| $\mathbf{B_{28}}$ | = | $- x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $- \left(a x_{23} + c z_{23} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}- c z_{23} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co XI |
| $\mathbf{B_{29}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + c z_{24} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co XII |
| $\mathbf{B_{30}}$ | = | $- x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $- \left(a x_{24} + c z_{24} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}- c z_{24} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Co XII |
| $\mathbf{B_{31}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + c z_{25} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c z_{25} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{32}}$ | = | $- x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $- \left(a x_{25} + c z_{25} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}- c z_{25} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{33}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + c z_{26} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{34}}$ | = | $- x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}- z_{26} \, \mathbf{a}_{3}$ | = | $- \left(a x_{26} + c z_{26} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}- c z_{26} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{35}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + c z_{27} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O III |
| $\mathbf{B_{36}}$ | = | $- x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}- z_{27} \, \mathbf{a}_{3}$ | = | $- \left(a x_{27} + c z_{27} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}- c z_{27} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O III |
| $\mathbf{B_{37}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + c z_{28} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IV |
| $\mathbf{B_{38}}$ | = | $- x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}- z_{28} \, \mathbf{a}_{3}$ | = | $- \left(a x_{28} + c z_{28} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}- c z_{28} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IV |
| $\mathbf{B_{39}}$ | = | $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + c z_{29} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O V |
| $\mathbf{B_{40}}$ | = | $- x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}- z_{29} \, \mathbf{a}_{3}$ | = | $- \left(a x_{29} + c z_{29} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}- c z_{29} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O V |
| $\mathbf{B_{41}}$ | = | $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + c z_{30} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VI |
| $\mathbf{B_{42}}$ | = | $- x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}- z_{30} \, \mathbf{a}_{3}$ | = | $- \left(a x_{30} + c z_{30} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}- c z_{30} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VI |
| $\mathbf{B_{43}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + c z_{31} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VII |
| $\mathbf{B_{44}}$ | = | $- x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}- z_{31} \, \mathbf{a}_{3}$ | = | $- \left(a x_{31} + c z_{31} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}- c z_{31} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VII |
| $\mathbf{B_{45}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + c z_{32} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VIII |
| $\mathbf{B_{46}}$ | = | $- x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}- z_{32} \, \mathbf{a}_{3}$ | = | $- \left(a x_{32} + c z_{32} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}- c z_{32} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O VIII |
| $\mathbf{B_{47}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + c z_{33} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IX |
| $\mathbf{B_{48}}$ | = | $- x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}- z_{33} \, \mathbf{a}_{3}$ | = | $- \left(a x_{33} + c z_{33} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}- c z_{33} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O IX |
| $\mathbf{B_{49}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + c z_{34} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O X |
| $\mathbf{B_{50}}$ | = | $- x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}- z_{34} \, \mathbf{a}_{3}$ | = | $- \left(a x_{34} + c z_{34} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}- c z_{34} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O X |
| $\mathbf{B_{51}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + c z_{35} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XI |
| $\mathbf{B_{52}}$ | = | $- x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}- z_{35} \, \mathbf{a}_{3}$ | = | $- \left(a x_{35} + c z_{35} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}- c z_{35} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XI |
| $\mathbf{B_{53}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + c z_{36} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XII |
| $\mathbf{B_{54}}$ | = | $- x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}- z_{36} \, \mathbf{a}_{3}$ | = | $- \left(a x_{36} + c z_{36} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}- c z_{36} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XII |
| $\mathbf{B_{55}}$ | = | $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ | = | $\left(a x_{37} + c z_{37} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIII |
| $\mathbf{B_{56}}$ | = | $- x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}- z_{37} \, \mathbf{a}_{3}$ | = | $- \left(a x_{37} + c z_{37} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}- c z_{37} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIII |
| $\mathbf{B_{57}}$ | = | $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ | = | $\left(a x_{38} + c z_{38} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIV |
| $\mathbf{B_{58}}$ | = | $- x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}- z_{38} \, \mathbf{a}_{3}$ | = | $- \left(a x_{38} + c z_{38} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}- c z_{38} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIV |
| $\mathbf{B_{59}}$ | = | $x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ | = | $\left(a x_{39} + c z_{39} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{39} \,\mathbf{\hat{y}}+c z_{39} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XV |
| $\mathbf{B_{60}}$ | = | $- x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}- z_{39} \, \mathbf{a}_{3}$ | = | $- \left(a x_{39} + c z_{39} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{39} \,\mathbf{\hat{y}}- c z_{39} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XV |
| $\mathbf{B_{61}}$ | = | $x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ | = | $\left(a x_{40} + c z_{40} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{40} \,\mathbf{\hat{y}}+c z_{40} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVI |
| $\mathbf{B_{62}}$ | = | $- x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}- z_{40} \, \mathbf{a}_{3}$ | = | $- \left(a x_{40} + c z_{40} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{40} \,\mathbf{\hat{y}}- c z_{40} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVI |
| $\mathbf{B_{63}}$ | = | $x_{41} \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}+z_{41} \, \mathbf{a}_{3}$ | = | $\left(a x_{41} + c z_{41} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{41} \,\mathbf{\hat{y}}+c z_{41} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVII |
| $\mathbf{B_{64}}$ | = | $- x_{41} \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}- z_{41} \, \mathbf{a}_{3}$ | = | $- \left(a x_{41} + c z_{41} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{41} \,\mathbf{\hat{y}}- c z_{41} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVII |
| $\mathbf{B_{65}}$ | = | $x_{42} \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}+z_{42} \, \mathbf{a}_{3}$ | = | $\left(a x_{42} + c z_{42} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{42} \,\mathbf{\hat{y}}+c z_{42} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVIII |
| $\mathbf{B_{66}}$ | = | $- x_{42} \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}- z_{42} \, \mathbf{a}_{3}$ | = | $- \left(a x_{42} + c z_{42} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{42} \,\mathbf{\hat{y}}- c z_{42} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XVIII |
| $\mathbf{B_{67}}$ | = | $x_{43} \, \mathbf{a}_{1}+y_{43} \, \mathbf{a}_{2}+z_{43} \, \mathbf{a}_{3}$ | = | $\left(a x_{43} + c z_{43} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{43} \,\mathbf{\hat{y}}+c z_{43} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIX |
| $\mathbf{B_{68}}$ | = | $- x_{43} \, \mathbf{a}_{1}+y_{43} \, \mathbf{a}_{2}- z_{43} \, \mathbf{a}_{3}$ | = | $- \left(a x_{43} + c z_{43} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{43} \,\mathbf{\hat{y}}- c z_{43} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XIX |
| $\mathbf{B_{69}}$ | = | $x_{44} \, \mathbf{a}_{1}+y_{44} \, \mathbf{a}_{2}+z_{44} \, \mathbf{a}_{3}$ | = | $\left(a x_{44} + c z_{44} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{44} \,\mathbf{\hat{y}}+c z_{44} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XX |
| $\mathbf{B_{70}}$ | = | $- x_{44} \, \mathbf{a}_{1}+y_{44} \, \mathbf{a}_{2}- z_{44} \, \mathbf{a}_{3}$ | = | $- \left(a x_{44} + c z_{44} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{44} \,\mathbf{\hat{y}}- c z_{44} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XX |
| $\mathbf{B_{71}}$ | = | $x_{45} \, \mathbf{a}_{1}+y_{45} \, \mathbf{a}_{2}+z_{45} \, \mathbf{a}_{3}$ | = | $\left(a x_{45} + c z_{45} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{45} \,\mathbf{\hat{y}}+c z_{45} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXI |
| $\mathbf{B_{72}}$ | = | $- x_{45} \, \mathbf{a}_{1}+y_{45} \, \mathbf{a}_{2}- z_{45} \, \mathbf{a}_{3}$ | = | $- \left(a x_{45} + c z_{45} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{45} \,\mathbf{\hat{y}}- c z_{45} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXI |
| $\mathbf{B_{73}}$ | = | $x_{46} \, \mathbf{a}_{1}+y_{46} \, \mathbf{a}_{2}+z_{46} \, \mathbf{a}_{3}$ | = | $\left(a x_{46} + c z_{46} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{46} \,\mathbf{\hat{y}}+c z_{46} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXII |
| $\mathbf{B_{74}}$ | = | $- x_{46} \, \mathbf{a}_{1}+y_{46} \, \mathbf{a}_{2}- z_{46} \, \mathbf{a}_{3}$ | = | $- \left(a x_{46} + c z_{46} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{46} \,\mathbf{\hat{y}}- c z_{46} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXII |
| $\mathbf{B_{75}}$ | = | $x_{47} \, \mathbf{a}_{1}+y_{47} \, \mathbf{a}_{2}+z_{47} \, \mathbf{a}_{3}$ | = | $\left(a x_{47} + c z_{47} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{47} \,\mathbf{\hat{y}}+c z_{47} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIII |
| $\mathbf{B_{76}}$ | = | $- x_{47} \, \mathbf{a}_{1}+y_{47} \, \mathbf{a}_{2}- z_{47} \, \mathbf{a}_{3}$ | = | $- \left(a x_{47} + c z_{47} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{47} \,\mathbf{\hat{y}}- c z_{47} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIII |
| $\mathbf{B_{77}}$ | = | $x_{48} \, \mathbf{a}_{1}+y_{48} \, \mathbf{a}_{2}+z_{48} \, \mathbf{a}_{3}$ | = | $\left(a x_{48} + c z_{48} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{48} \,\mathbf{\hat{y}}+c z_{48} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIV |
| $\mathbf{B_{78}}$ | = | $- x_{48} \, \mathbf{a}_{1}+y_{48} \, \mathbf{a}_{2}- z_{48} \, \mathbf{a}_{3}$ | = | $- \left(a x_{48} + c z_{48} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{48} \,\mathbf{\hat{y}}- c z_{48} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIV |
| $\mathbf{B_{79}}$ | = | $x_{49} \, \mathbf{a}_{1}+y_{49} \, \mathbf{a}_{2}+z_{49} \, \mathbf{a}_{3}$ | = | $\left(a x_{49} + c z_{49} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{49} \,\mathbf{\hat{y}}+c z_{49} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXV |
| $\mathbf{B_{80}}$ | = | $- x_{49} \, \mathbf{a}_{1}+y_{49} \, \mathbf{a}_{2}- z_{49} \, \mathbf{a}_{3}$ | = | $- \left(a x_{49} + c z_{49} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{49} \,\mathbf{\hat{y}}- c z_{49} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXV |
| $\mathbf{B_{81}}$ | = | $x_{50} \, \mathbf{a}_{1}+y_{50} \, \mathbf{a}_{2}+z_{50} \, \mathbf{a}_{3}$ | = | $\left(a x_{50} + c z_{50} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{50} \,\mathbf{\hat{y}}+c z_{50} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVI |
| $\mathbf{B_{82}}$ | = | $- x_{50} \, \mathbf{a}_{1}+y_{50} \, \mathbf{a}_{2}- z_{50} \, \mathbf{a}_{3}$ | = | $- \left(a x_{50} + c z_{50} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{50} \,\mathbf{\hat{y}}- c z_{50} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVI |
| $\mathbf{B_{83}}$ | = | $x_{51} \, \mathbf{a}_{1}+y_{51} \, \mathbf{a}_{2}+z_{51} \, \mathbf{a}_{3}$ | = | $\left(a x_{51} + c z_{51} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{51} \,\mathbf{\hat{y}}+c z_{51} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVII |
| $\mathbf{B_{84}}$ | = | $- x_{51} \, \mathbf{a}_{1}+y_{51} \, \mathbf{a}_{2}- z_{51} \, \mathbf{a}_{3}$ | = | $- \left(a x_{51} + c z_{51} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{51} \,\mathbf{\hat{y}}- c z_{51} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVII |
| $\mathbf{B_{85}}$ | = | $x_{52} \, \mathbf{a}_{1}+y_{52} \, \mathbf{a}_{2}+z_{52} \, \mathbf{a}_{3}$ | = | $\left(a x_{52} + c z_{52} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{52} \,\mathbf{\hat{y}}+c z_{52} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVIII |
| $\mathbf{B_{86}}$ | = | $- x_{52} \, \mathbf{a}_{1}+y_{52} \, \mathbf{a}_{2}- z_{52} \, \mathbf{a}_{3}$ | = | $- \left(a x_{52} + c z_{52} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{52} \,\mathbf{\hat{y}}- c z_{52} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXVIII |
| $\mathbf{B_{87}}$ | = | $x_{53} \, \mathbf{a}_{1}+y_{53} \, \mathbf{a}_{2}+z_{53} \, \mathbf{a}_{3}$ | = | $\left(a x_{53} + c z_{53} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{53} \,\mathbf{\hat{y}}+c z_{53} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIX |
| $\mathbf{B_{88}}$ | = | $- x_{53} \, \mathbf{a}_{1}+y_{53} \, \mathbf{a}_{2}- z_{53} \, \mathbf{a}_{3}$ | = | $- \left(a x_{53} + c z_{53} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{53} \,\mathbf{\hat{y}}- c z_{53} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXIX |
| $\mathbf{B_{89}}$ | = | $x_{54} \, \mathbf{a}_{1}+y_{54} \, \mathbf{a}_{2}+z_{54} \, \mathbf{a}_{3}$ | = | $\left(a x_{54} + c z_{54} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{54} \,\mathbf{\hat{y}}+c z_{54} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXX |
| $\mathbf{B_{90}}$ | = | $- x_{54} \, \mathbf{a}_{1}+y_{54} \, \mathbf{a}_{2}- z_{54} \, \mathbf{a}_{3}$ | = | $- \left(a x_{54} + c z_{54} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{54} \,\mathbf{\hat{y}}- c z_{54} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXX |
| $\mathbf{B_{91}}$ | = | $x_{55} \, \mathbf{a}_{1}+y_{55} \, \mathbf{a}_{2}+z_{55} \, \mathbf{a}_{3}$ | = | $\left(a x_{55} + c z_{55} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{55} \,\mathbf{\hat{y}}+c z_{55} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXI |
| $\mathbf{B_{92}}$ | = | $- x_{55} \, \mathbf{a}_{1}+y_{55} \, \mathbf{a}_{2}- z_{55} \, \mathbf{a}_{3}$ | = | $- \left(a x_{55} + c z_{55} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{55} \,\mathbf{\hat{y}}- c z_{55} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXI |
| $\mathbf{B_{93}}$ | = | $x_{56} \, \mathbf{a}_{1}+y_{56} \, \mathbf{a}_{2}+z_{56} \, \mathbf{a}_{3}$ | = | $\left(a x_{56} + c z_{56} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{56} \,\mathbf{\hat{y}}+c z_{56} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXII |
| $\mathbf{B_{94}}$ | = | $- x_{56} \, \mathbf{a}_{1}+y_{56} \, \mathbf{a}_{2}- z_{56} \, \mathbf{a}_{3}$ | = | $- \left(a x_{56} + c z_{56} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{56} \,\mathbf{\hat{y}}- c z_{56} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXII |
| $\mathbf{B_{95}}$ | = | $x_{57} \, \mathbf{a}_{1}+y_{57} \, \mathbf{a}_{2}+z_{57} \, \mathbf{a}_{3}$ | = | $\left(a x_{57} + c z_{57} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{57} \,\mathbf{\hat{y}}+c z_{57} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIII |
| $\mathbf{B_{96}}$ | = | $- x_{57} \, \mathbf{a}_{1}+y_{57} \, \mathbf{a}_{2}- z_{57} \, \mathbf{a}_{3}$ | = | $- \left(a x_{57} + c z_{57} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{57} \,\mathbf{\hat{y}}- c z_{57} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIII |
| $\mathbf{B_{97}}$ | = | $x_{58} \, \mathbf{a}_{1}+y_{58} \, \mathbf{a}_{2}+z_{58} \, \mathbf{a}_{3}$ | = | $\left(a x_{58} + c z_{58} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{58} \,\mathbf{\hat{y}}+c z_{58} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIV |
| $\mathbf{B_{98}}$ | = | $- x_{58} \, \mathbf{a}_{1}+y_{58} \, \mathbf{a}_{2}- z_{58} \, \mathbf{a}_{3}$ | = | $- \left(a x_{58} + c z_{58} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{58} \,\mathbf{\hat{y}}- c z_{58} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIV |
| $\mathbf{B_{99}}$ | = | $x_{59} \, \mathbf{a}_{1}+y_{59} \, \mathbf{a}_{2}+z_{59} \, \mathbf{a}_{3}$ | = | $\left(a x_{59} + c z_{59} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{59} \,\mathbf{\hat{y}}+c z_{59} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXV |
| $\mathbf{B_{100}}$ | = | $- x_{59} \, \mathbf{a}_{1}+y_{59} \, \mathbf{a}_{2}- z_{59} \, \mathbf{a}_{3}$ | = | $- \left(a x_{59} + c z_{59} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{59} \,\mathbf{\hat{y}}- c z_{59} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXV |
| $\mathbf{B_{101}}$ | = | $x_{60} \, \mathbf{a}_{1}+y_{60} \, \mathbf{a}_{2}+z_{60} \, \mathbf{a}_{3}$ | = | $\left(a x_{60} + c z_{60} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{60} \,\mathbf{\hat{y}}+c z_{60} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVI |
| $\mathbf{B_{102}}$ | = | $- x_{60} \, \mathbf{a}_{1}+y_{60} \, \mathbf{a}_{2}- z_{60} \, \mathbf{a}_{3}$ | = | $- \left(a x_{60} + c z_{60} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{60} \,\mathbf{\hat{y}}- c z_{60} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVI |
| $\mathbf{B_{103}}$ | = | $x_{61} \, \mathbf{a}_{1}+y_{61} \, \mathbf{a}_{2}+z_{61} \, \mathbf{a}_{3}$ | = | $\left(a x_{61} + c z_{61} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{61} \,\mathbf{\hat{y}}+c z_{61} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVII |
| $\mathbf{B_{104}}$ | = | $- x_{61} \, \mathbf{a}_{1}+y_{61} \, \mathbf{a}_{2}- z_{61} \, \mathbf{a}_{3}$ | = | $- \left(a x_{61} + c z_{61} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{61} \,\mathbf{\hat{y}}- c z_{61} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVII |
| $\mathbf{B_{105}}$ | = | $x_{62} \, \mathbf{a}_{1}+y_{62} \, \mathbf{a}_{2}+z_{62} \, \mathbf{a}_{3}$ | = | $\left(a x_{62} + c z_{62} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{62} \,\mathbf{\hat{y}}+c z_{62} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVIII |
| $\mathbf{B_{106}}$ | = | $- x_{62} \, \mathbf{a}_{1}+y_{62} \, \mathbf{a}_{2}- z_{62} \, \mathbf{a}_{3}$ | = | $- \left(a x_{62} + c z_{62} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{62} \,\mathbf{\hat{y}}- c z_{62} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXVIII |
| $\mathbf{B_{107}}$ | = | $x_{63} \, \mathbf{a}_{1}+y_{63} \, \mathbf{a}_{2}+z_{63} \, \mathbf{a}_{3}$ | = | $\left(a x_{63} + c z_{63} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{63} \,\mathbf{\hat{y}}+c z_{63} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIX |
| $\mathbf{B_{108}}$ | = | $- x_{63} \, \mathbf{a}_{1}+y_{63} \, \mathbf{a}_{2}- z_{63} \, \mathbf{a}_{3}$ | = | $- \left(a x_{63} + c z_{63} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{63} \,\mathbf{\hat{y}}- c z_{63} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XXXIX |
| $\mathbf{B_{109}}$ | = | $x_{64} \, \mathbf{a}_{1}+y_{64} \, \mathbf{a}_{2}+z_{64} \, \mathbf{a}_{3}$ | = | $\left(a x_{64} + c z_{64} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{64} \,\mathbf{\hat{y}}+c z_{64} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XL |
| $\mathbf{B_{110}}$ | = | $- x_{64} \, \mathbf{a}_{1}+y_{64} \, \mathbf{a}_{2}- z_{64} \, \mathbf{a}_{3}$ | = | $- \left(a x_{64} + c z_{64} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{64} \,\mathbf{\hat{y}}- c z_{64} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XL |
| $\mathbf{B_{111}}$ | = | $x_{65} \, \mathbf{a}_{1}+y_{65} \, \mathbf{a}_{2}+z_{65} \, \mathbf{a}_{3}$ | = | $\left(a x_{65} + c z_{65} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{65} \,\mathbf{\hat{y}}+c z_{65} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XLI |
| $\mathbf{B_{112}}$ | = | $- x_{65} \, \mathbf{a}_{1}+y_{65} \, \mathbf{a}_{2}- z_{65} \, \mathbf{a}_{3}$ | = | $- \left(a x_{65} + c z_{65} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{65} \,\mathbf{\hat{y}}- c z_{65} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XLI |
| $\mathbf{B_{113}}$ | = | $x_{66} \, \mathbf{a}_{1}+y_{66} \, \mathbf{a}_{2}+z_{66} \, \mathbf{a}_{3}$ | = | $\left(a x_{66} + c z_{66} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{66} \,\mathbf{\hat{y}}+c z_{66} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XLII |
| $\mathbf{B_{114}}$ | = | $- x_{66} \, \mathbf{a}_{1}+y_{66} \, \mathbf{a}_{2}- z_{66} \, \mathbf{a}_{3}$ | = | $- \left(a x_{66} + c z_{66} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{66} \,\mathbf{\hat{y}}- c z_{66} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | O XLII |
| $\mathbf{B_{115}}$ | = | $x_{67} \, \mathbf{a}_{1}+y_{67} \, \mathbf{a}_{2}+z_{67} \, \mathbf{a}_{3}$ | = | $\left(a x_{67} + c z_{67} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{67} \,\mathbf{\hat{y}}+c z_{67} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P I |
| $\mathbf{B_{116}}$ | = | $- x_{67} \, \mathbf{a}_{1}+y_{67} \, \mathbf{a}_{2}- z_{67} \, \mathbf{a}_{3}$ | = | $- \left(a x_{67} + c z_{67} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{67} \,\mathbf{\hat{y}}- c z_{67} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P I |
| $\mathbf{B_{117}}$ | = | $x_{68} \, \mathbf{a}_{1}+y_{68} \, \mathbf{a}_{2}+z_{68} \, \mathbf{a}_{3}$ | = | $\left(a x_{68} + c z_{68} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{68} \,\mathbf{\hat{y}}+c z_{68} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P II |
| $\mathbf{B_{118}}$ | = | $- x_{68} \, \mathbf{a}_{1}+y_{68} \, \mathbf{a}_{2}- z_{68} \, \mathbf{a}_{3}$ | = | $- \left(a x_{68} + c z_{68} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{68} \,\mathbf{\hat{y}}- c z_{68} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P II |
| $\mathbf{B_{119}}$ | = | $x_{69} \, \mathbf{a}_{1}+y_{69} \, \mathbf{a}_{2}+z_{69} \, \mathbf{a}_{3}$ | = | $\left(a x_{69} + c z_{69} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{69} \,\mathbf{\hat{y}}+c z_{69} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P III |
| $\mathbf{B_{120}}$ | = | $- x_{69} \, \mathbf{a}_{1}+y_{69} \, \mathbf{a}_{2}- z_{69} \, \mathbf{a}_{3}$ | = | $- \left(a x_{69} + c z_{69} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{69} \,\mathbf{\hat{y}}- c z_{69} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P III |
| $\mathbf{B_{121}}$ | = | $x_{70} \, \mathbf{a}_{1}+y_{70} \, \mathbf{a}_{2}+z_{70} \, \mathbf{a}_{3}$ | = | $\left(a x_{70} + c z_{70} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{70} \,\mathbf{\hat{y}}+c z_{70} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P IV |
| $\mathbf{B_{122}}$ | = | $- x_{70} \, \mathbf{a}_{1}+y_{70} \, \mathbf{a}_{2}- z_{70} \, \mathbf{a}_{3}$ | = | $- \left(a x_{70} + c z_{70} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{70} \,\mathbf{\hat{y}}- c z_{70} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P IV |
| $\mathbf{B_{123}}$ | = | $x_{71} \, \mathbf{a}_{1}+y_{71} \, \mathbf{a}_{2}+z_{71} \, \mathbf{a}_{3}$ | = | $\left(a x_{71} + c z_{71} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{71} \,\mathbf{\hat{y}}+c z_{71} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P V |
| $\mathbf{B_{124}}$ | = | $- x_{71} \, \mathbf{a}_{1}+y_{71} \, \mathbf{a}_{2}- z_{71} \, \mathbf{a}_{3}$ | = | $- \left(a x_{71} + c z_{71} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{71} \,\mathbf{\hat{y}}- c z_{71} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P V |
| $\mathbf{B_{125}}$ | = | $x_{72} \, \mathbf{a}_{1}+y_{72} \, \mathbf{a}_{2}+z_{72} \, \mathbf{a}_{3}$ | = | $\left(a x_{72} + c z_{72} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{72} \,\mathbf{\hat{y}}+c z_{72} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P VI |
| $\mathbf{B_{126}}$ | = | $- x_{72} \, \mathbf{a}_{1}+y_{72} \, \mathbf{a}_{2}- z_{72} \, \mathbf{a}_{3}$ | = | $- \left(a x_{72} + c z_{72} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{72} \,\mathbf{\hat{y}}- c z_{72} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | P VI |
| $\mathbf{B_{127}}$ | = | $x_{73} \, \mathbf{a}_{1}+y_{73} \, \mathbf{a}_{2}+z_{73} \, \mathbf{a}_{3}$ | = | $\left(a x_{73} + c z_{73} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{73} \,\mathbf{\hat{y}}+c z_{73} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb VII |
| $\mathbf{B_{128}}$ | = | $- x_{73} \, \mathbf{a}_{1}+y_{73} \, \mathbf{a}_{2}- z_{73} \, \mathbf{a}_{3}$ | = | $- \left(a x_{73} + c z_{73} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{73} \,\mathbf{\hat{y}}- c z_{73} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb VII |
| $\mathbf{B_{129}}$ | = | $x_{74} \, \mathbf{a}_{1}+y_{74} \, \mathbf{a}_{2}+z_{74} \, \mathbf{a}_{3}$ | = | $\left(a x_{74} + c z_{74} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{74} \,\mathbf{\hat{y}}+c z_{74} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb VIII |
| $\mathbf{B_{130}}$ | = | $- x_{74} \, \mathbf{a}_{1}+y_{74} \, \mathbf{a}_{2}- z_{74} \, \mathbf{a}_{3}$ | = | $- \left(a x_{74} + c z_{74} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{74} \,\mathbf{\hat{y}}- c z_{74} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb VIII |
| $\mathbf{B_{131}}$ | = | $x_{75} \, \mathbf{a}_{1}+y_{75} \, \mathbf{a}_{2}+z_{75} \, \mathbf{a}_{3}$ | = | $\left(a x_{75} + c z_{75} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{75} \,\mathbf{\hat{y}}+c z_{75} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb IX |
| $\mathbf{B_{132}}$ | = | $- x_{75} \, \mathbf{a}_{1}+y_{75} \, \mathbf{a}_{2}- z_{75} \, \mathbf{a}_{3}$ | = | $- \left(a x_{75} + c z_{75} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{75} \,\mathbf{\hat{y}}- c z_{75} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb IX |
| $\mathbf{B_{133}}$ | = | $x_{76} \, \mathbf{a}_{1}+y_{76} \, \mathbf{a}_{2}+z_{76} \, \mathbf{a}_{3}$ | = | $\left(a x_{76} + c z_{76} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{76} \,\mathbf{\hat{y}}+c z_{76} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb X |
| $\mathbf{B_{134}}$ | = | $- x_{76} \, \mathbf{a}_{1}+y_{76} \, \mathbf{a}_{2}- z_{76} \, \mathbf{a}_{3}$ | = | $- \left(a x_{76} + c z_{76} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{76} \,\mathbf{\hat{y}}- c z_{76} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb X |
| $\mathbf{B_{135}}$ | = | $x_{77} \, \mathbf{a}_{1}+y_{77} \, \mathbf{a}_{2}+z_{77} \, \mathbf{a}_{3}$ | = | $\left(a x_{77} + c z_{77} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{77} \,\mathbf{\hat{y}}+c z_{77} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb XI |
| $\mathbf{B_{136}}$ | = | $- x_{77} \, \mathbf{a}_{1}+y_{77} \, \mathbf{a}_{2}- z_{77} \, \mathbf{a}_{3}$ | = | $- \left(a x_{77} + c z_{77} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{77} \,\mathbf{\hat{y}}- c z_{77} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb XI |
| $\mathbf{B_{137}}$ | = | $x_{78} \, \mathbf{a}_{1}+y_{78} \, \mathbf{a}_{2}+z_{78} \, \mathbf{a}_{3}$ | = | $\left(a x_{78} + c z_{78} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{78} \,\mathbf{\hat{y}}+c z_{78} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb XII |
| $\mathbf{B_{138}}$ | = | $- x_{78} \, \mathbf{a}_{1}+y_{78} \, \mathbf{a}_{2}- z_{78} \, \mathbf{a}_{3}$ | = | $- \left(a x_{78} + c z_{78} \cos{\beta}\right) \,\mathbf{\hat{x}}+b y_{78} \,\mathbf{\hat{y}}- c z_{78} \sin{\beta} \,\mathbf{\hat{z}}$ | (2e) | Pb XII |
References
- J. W. Krizan, C. de la Cruz, N. H. Andersen, and R. J. Cava, Crystal structure and magnetic properties of the Ba$_{3}$TeCo$_{3}$P$_{2}$O$_{14}$, Pb$_{3}$TeCo$_{3}$P$_{2}$O$_{14}$, and Pb$_{3}$TeCo$_{3}$V$_{2}$O$_{14}$ langasites, Journal of Solid State Chemistry 203, 310–320 (2013), doi:10.1016/j.jssc.2013.04.035.
Prototype Generator
aflow --proto=A3B14C2D3E_mP138_3_3c3d6e_42e_6e_3a3b6e_3a3b --params=$a,b/a,c/a,\beta,y_{1},y_{2},y_{3},y_{4},y_{5},y_{6},y_{7},y_{8},y_{9},y_{10},y_{11},y_{12},y_{13},y_{14},y_{15},y_{16},y_{17},y_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28},x_{29},y_{29},z_{29},x_{30},y_{30},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38},x_{39},y_{39},z_{39},x_{40},y_{40},z_{40},x_{41},y_{41},z_{41},x_{42},y_{42},z_{42},x_{43},y_{43},z_{43},x_{44},y_{44},z_{44},x_{45},y_{45},z_{45},x_{46},y_{46},z_{46},x_{47},y_{47},z_{47},x_{48},y_{48},z_{48},x_{49},y_{49},z_{49},x_{50},y_{50},z_{50},x_{51},y_{51},z_{51},x_{52},y_{52},z_{52},x_{53},y_{53},z_{53},x_{54},y_{54},z_{54},x_{55},y_{55},z_{55},x_{56},y_{56},z_{56},x_{57},y_{57},z_{57},x_{58},y_{58},z_{58},x_{59},y_{59},z_{59},x_{60},y_{60},z_{60},x_{61},y_{61},z_{61},x_{62},y_{62},z_{62},x_{63},y_{63},z_{63},x_{64},y_{64},z_{64},x_{65},y_{65},z_{65},x_{66},y_{66},z_{66},x_{67},y_{67},z_{67},x_{68},y_{68},z_{68},x_{69},y_{69},z_{69},x_{70},y_{70},z_{70},x_{71},y_{71},z_{71},x_{72},y_{72},z_{72},x_{73},y_{73},z_{73},x_{74},y_{74},z_{74},x_{75},y_{75},z_{75},x_{76},y_{76},z_{76},x_{77},y_{77},z_{77},x_{78},y_{78},z_{78}$