AFLOW Prototype: A11B7_aP72_2_22i_14i-001
If you are using this page, please cite:
H. Eckert, S. Divilov, M. J. Mehl, D. Hicks, A. C. Zettel, M. Esters. X. Campilongo and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 4. Submitted to Computational Materials Science.
Links to this page
https://aflow.org/p/C9KZ
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https://aflow.org/p/A11B7_aP72_2_22i_14i-001
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PDF Version
Prototype | C$_{11}$H$_{7}$ |
AFLOW prototype label | A11B7_aP72_2_22i_14i-001 |
Mineral name | pentacene |
CCDC | 1818858 |
Pearson symbol | aP72 |
Space group number | 2 |
Space group symbol | $P\overline{1}$ |
AFLOW prototype command |
aflow --proto=A11B7_aP72_2_22i_14i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak \alpha, \allowbreak \beta, \allowbreak \gamma, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{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}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{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}$ |
Basis vectors
Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
---|---|---|---|---|---|---|
$\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}+\left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}+c_{z} z_{1} \,\mathbf{\hat{z}}$ | (2i) | C I |
$\mathbf{B_{2}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \left(a x_{1} + b y_{1} \cos{\gamma} + c_{x} z_{1}\right) \,\mathbf{\hat{x}}- \left(b y_{1} \sin{\gamma} + c_{y} z_{1}\right) \,\mathbf{\hat{y}}- c_{z} z_{1} \,\mathbf{\hat{z}}$ | (2i) | C I |
$\mathbf{B_{3}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}+\left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}+c_{z} z_{2} \,\mathbf{\hat{z}}$ | (2i) | C II |
$\mathbf{B_{4}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \left(a x_{2} + b y_{2} \cos{\gamma} + c_{x} z_{2}\right) \,\mathbf{\hat{x}}- \left(b y_{2} \sin{\gamma} + c_{y} z_{2}\right) \,\mathbf{\hat{y}}- c_{z} z_{2} \,\mathbf{\hat{z}}$ | (2i) | C II |
$\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}+\left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}+c_{z} z_{3} \,\mathbf{\hat{z}}$ | (2i) | C III |
$\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \left(a x_{3} + b y_{3} \cos{\gamma} + c_{x} z_{3}\right) \,\mathbf{\hat{x}}- \left(b y_{3} \sin{\gamma} + c_{y} z_{3}\right) \,\mathbf{\hat{y}}- c_{z} z_{3} \,\mathbf{\hat{z}}$ | (2i) | C III |
$\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\left(a x_{4} + b y_{4} \cos{\gamma} + c_{x} z_{4}\right) \,\mathbf{\hat{x}}+\left(b y_{4} \sin{\gamma} + c_{y} z_{4}\right) \,\mathbf{\hat{y}}+c_{z} z_{4} \,\mathbf{\hat{z}}$ | (2i) | C IV |
$\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- \left(a x_{4} + b y_{4} \cos{\gamma} + c_{x} z_{4}\right) \,\mathbf{\hat{x}}- \left(b y_{4} \sin{\gamma} + c_{y} z_{4}\right) \,\mathbf{\hat{y}}- c_{z} z_{4} \,\mathbf{\hat{z}}$ | (2i) | C IV |
$\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\left(a x_{5} + b y_{5} \cos{\gamma} + c_{x} z_{5}\right) \,\mathbf{\hat{x}}+\left(b y_{5} \sin{\gamma} + c_{y} z_{5}\right) \,\mathbf{\hat{y}}+c_{z} z_{5} \,\mathbf{\hat{z}}$ | (2i) | C V |
$\mathbf{B_{10}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $- \left(a x_{5} + b y_{5} \cos{\gamma} + c_{x} z_{5}\right) \,\mathbf{\hat{x}}- \left(b y_{5} \sin{\gamma} + c_{y} z_{5}\right) \,\mathbf{\hat{y}}- c_{z} z_{5} \,\mathbf{\hat{z}}$ | (2i) | C V |
$\mathbf{B_{11}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\left(a x_{6} + b y_{6} \cos{\gamma} + c_{x} z_{6}\right) \,\mathbf{\hat{x}}+\left(b y_{6} \sin{\gamma} + c_{y} z_{6}\right) \,\mathbf{\hat{y}}+c_{z} z_{6} \,\mathbf{\hat{z}}$ | (2i) | C VI |
$\mathbf{B_{12}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $- \left(a x_{6} + b y_{6} \cos{\gamma} + c_{x} z_{6}\right) \,\mathbf{\hat{x}}- \left(b y_{6} \sin{\gamma} + c_{y} z_{6}\right) \,\mathbf{\hat{y}}- c_{z} z_{6} \,\mathbf{\hat{z}}$ | (2i) | C VI |
$\mathbf{B_{13}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\left(a x_{7} + b y_{7} \cos{\gamma} + c_{x} z_{7}\right) \,\mathbf{\hat{x}}+\left(b y_{7} \sin{\gamma} + c_{y} z_{7}\right) \,\mathbf{\hat{y}}+c_{z} z_{7} \,\mathbf{\hat{z}}$ | (2i) | C VII |
$\mathbf{B_{14}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $- \left(a x_{7} + b y_{7} \cos{\gamma} + c_{x} z_{7}\right) \,\mathbf{\hat{x}}- \left(b y_{7} \sin{\gamma} + c_{y} z_{7}\right) \,\mathbf{\hat{y}}- c_{z} z_{7} \,\mathbf{\hat{z}}$ | (2i) | C VII |
$\mathbf{B_{15}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\left(a x_{8} + b y_{8} \cos{\gamma} + c_{x} z_{8}\right) \,\mathbf{\hat{x}}+\left(b y_{8} \sin{\gamma} + c_{y} z_{8}\right) \,\mathbf{\hat{y}}+c_{z} z_{8} \,\mathbf{\hat{z}}$ | (2i) | C VIII |
$\mathbf{B_{16}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $- \left(a x_{8} + b y_{8} \cos{\gamma} + c_{x} z_{8}\right) \,\mathbf{\hat{x}}- \left(b y_{8} \sin{\gamma} + c_{y} z_{8}\right) \,\mathbf{\hat{y}}- c_{z} z_{8} \,\mathbf{\hat{z}}$ | (2i) | C VIII |
$\mathbf{B_{17}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\left(a x_{9} + b y_{9} \cos{\gamma} + c_{x} z_{9}\right) \,\mathbf{\hat{x}}+\left(b y_{9} \sin{\gamma} + c_{y} z_{9}\right) \,\mathbf{\hat{y}}+c_{z} z_{9} \,\mathbf{\hat{z}}$ | (2i) | C IX |
$\mathbf{B_{18}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $- \left(a x_{9} + b y_{9} \cos{\gamma} + c_{x} z_{9}\right) \,\mathbf{\hat{x}}- \left(b y_{9} \sin{\gamma} + c_{y} z_{9}\right) \,\mathbf{\hat{y}}- c_{z} z_{9} \,\mathbf{\hat{z}}$ | (2i) | C IX |
$\mathbf{B_{19}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\left(a x_{10} + b y_{10} \cos{\gamma} + c_{x} z_{10}\right) \,\mathbf{\hat{x}}+\left(b y_{10} \sin{\gamma} + c_{y} z_{10}\right) \,\mathbf{\hat{y}}+c_{z} z_{10} \,\mathbf{\hat{z}}$ | (2i) | C X |
$\mathbf{B_{20}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $- \left(a x_{10} + b y_{10} \cos{\gamma} + c_{x} z_{10}\right) \,\mathbf{\hat{x}}- \left(b y_{10} \sin{\gamma} + c_{y} z_{10}\right) \,\mathbf{\hat{y}}- c_{z} z_{10} \,\mathbf{\hat{z}}$ | (2i) | C X |
$\mathbf{B_{21}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\left(a x_{11} + b y_{11} \cos{\gamma} + c_{x} z_{11}\right) \,\mathbf{\hat{x}}+\left(b y_{11} \sin{\gamma} + c_{y} z_{11}\right) \,\mathbf{\hat{y}}+c_{z} z_{11} \,\mathbf{\hat{z}}$ | (2i) | C XI |
$\mathbf{B_{22}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $- \left(a x_{11} + b y_{11} \cos{\gamma} + c_{x} z_{11}\right) \,\mathbf{\hat{x}}- \left(b y_{11} \sin{\gamma} + c_{y} z_{11}\right) \,\mathbf{\hat{y}}- c_{z} z_{11} \,\mathbf{\hat{z}}$ | (2i) | C XI |
$\mathbf{B_{23}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\left(a x_{12} + b y_{12} \cos{\gamma} + c_{x} z_{12}\right) \,\mathbf{\hat{x}}+\left(b y_{12} \sin{\gamma} + c_{y} z_{12}\right) \,\mathbf{\hat{y}}+c_{z} z_{12} \,\mathbf{\hat{z}}$ | (2i) | C XII |
$\mathbf{B_{24}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $- \left(a x_{12} + b y_{12} \cos{\gamma} + c_{x} z_{12}\right) \,\mathbf{\hat{x}}- \left(b y_{12} \sin{\gamma} + c_{y} z_{12}\right) \,\mathbf{\hat{y}}- c_{z} z_{12} \,\mathbf{\hat{z}}$ | (2i) | C XII |
$\mathbf{B_{25}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\left(a x_{13} + b y_{13} \cos{\gamma} + c_{x} z_{13}\right) \,\mathbf{\hat{x}}+\left(b y_{13} \sin{\gamma} + c_{y} z_{13}\right) \,\mathbf{\hat{y}}+c_{z} z_{13} \,\mathbf{\hat{z}}$ | (2i) | C XIII |
$\mathbf{B_{26}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $- \left(a x_{13} + b y_{13} \cos{\gamma} + c_{x} z_{13}\right) \,\mathbf{\hat{x}}- \left(b y_{13} \sin{\gamma} + c_{y} z_{13}\right) \,\mathbf{\hat{y}}- c_{z} z_{13} \,\mathbf{\hat{z}}$ | (2i) | C XIII |
$\mathbf{B_{27}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\left(a x_{14} + b y_{14} \cos{\gamma} + c_{x} z_{14}\right) \,\mathbf{\hat{x}}+\left(b y_{14} \sin{\gamma} + c_{y} z_{14}\right) \,\mathbf{\hat{y}}+c_{z} z_{14} \,\mathbf{\hat{z}}$ | (2i) | C XIV |
$\mathbf{B_{28}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- \left(a x_{14} + b y_{14} \cos{\gamma} + c_{x} z_{14}\right) \,\mathbf{\hat{x}}- \left(b y_{14} \sin{\gamma} + c_{y} z_{14}\right) \,\mathbf{\hat{y}}- c_{z} z_{14} \,\mathbf{\hat{z}}$ | (2i) | C XIV |
$\mathbf{B_{29}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\left(a x_{15} + b y_{15} \cos{\gamma} + c_{x} z_{15}\right) \,\mathbf{\hat{x}}+\left(b y_{15} \sin{\gamma} + c_{y} z_{15}\right) \,\mathbf{\hat{y}}+c_{z} z_{15} \,\mathbf{\hat{z}}$ | (2i) | C XV |
$\mathbf{B_{30}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- \left(a x_{15} + b y_{15} \cos{\gamma} + c_{x} z_{15}\right) \,\mathbf{\hat{x}}- \left(b y_{15} \sin{\gamma} + c_{y} z_{15}\right) \,\mathbf{\hat{y}}- c_{z} z_{15} \,\mathbf{\hat{z}}$ | (2i) | C XV |
$\mathbf{B_{31}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\left(a x_{16} + b y_{16} \cos{\gamma} + c_{x} z_{16}\right) \,\mathbf{\hat{x}}+\left(b y_{16} \sin{\gamma} + c_{y} z_{16}\right) \,\mathbf{\hat{y}}+c_{z} z_{16} \,\mathbf{\hat{z}}$ | (2i) | C XVI |
$\mathbf{B_{32}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $- \left(a x_{16} + b y_{16} \cos{\gamma} + c_{x} z_{16}\right) \,\mathbf{\hat{x}}- \left(b y_{16} \sin{\gamma} + c_{y} z_{16}\right) \,\mathbf{\hat{y}}- c_{z} z_{16} \,\mathbf{\hat{z}}$ | (2i) | C XVI |
$\mathbf{B_{33}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $\left(a x_{17} + b y_{17} \cos{\gamma} + c_{x} z_{17}\right) \,\mathbf{\hat{x}}+\left(b y_{17} \sin{\gamma} + c_{y} z_{17}\right) \,\mathbf{\hat{y}}+c_{z} z_{17} \,\mathbf{\hat{z}}$ | (2i) | C XVII |
$\mathbf{B_{34}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $- \left(a x_{17} + b y_{17} \cos{\gamma} + c_{x} z_{17}\right) \,\mathbf{\hat{x}}- \left(b y_{17} \sin{\gamma} + c_{y} z_{17}\right) \,\mathbf{\hat{y}}- c_{z} z_{17} \,\mathbf{\hat{z}}$ | (2i) | C XVII |
$\mathbf{B_{35}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $\left(a x_{18} + b y_{18} \cos{\gamma} + c_{x} z_{18}\right) \,\mathbf{\hat{x}}+\left(b y_{18} \sin{\gamma} + c_{y} z_{18}\right) \,\mathbf{\hat{y}}+c_{z} z_{18} \,\mathbf{\hat{z}}$ | (2i) | C XVIII |
$\mathbf{B_{36}}$ | = | $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $- \left(a x_{18} + b y_{18} \cos{\gamma} + c_{x} z_{18}\right) \,\mathbf{\hat{x}}- \left(b y_{18} \sin{\gamma} + c_{y} z_{18}\right) \,\mathbf{\hat{y}}- c_{z} z_{18} \,\mathbf{\hat{z}}$ | (2i) | C XVIII |
$\mathbf{B_{37}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $\left(a x_{19} + b y_{19} \cos{\gamma} + c_{x} z_{19}\right) \,\mathbf{\hat{x}}+\left(b y_{19} \sin{\gamma} + c_{y} z_{19}\right) \,\mathbf{\hat{y}}+c_{z} z_{19} \,\mathbf{\hat{z}}$ | (2i) | C XIX |
$\mathbf{B_{38}}$ | = | $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $- \left(a x_{19} + b y_{19} \cos{\gamma} + c_{x} z_{19}\right) \,\mathbf{\hat{x}}- \left(b y_{19} \sin{\gamma} + c_{y} z_{19}\right) \,\mathbf{\hat{y}}- c_{z} z_{19} \,\mathbf{\hat{z}}$ | (2i) | C XIX |
$\mathbf{B_{39}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $\left(a x_{20} + b y_{20} \cos{\gamma} + c_{x} z_{20}\right) \,\mathbf{\hat{x}}+\left(b y_{20} \sin{\gamma} + c_{y} z_{20}\right) \,\mathbf{\hat{y}}+c_{z} z_{20} \,\mathbf{\hat{z}}$ | (2i) | C XX |
$\mathbf{B_{40}}$ | = | $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $- \left(a x_{20} + b y_{20} \cos{\gamma} + c_{x} z_{20}\right) \,\mathbf{\hat{x}}- \left(b y_{20} \sin{\gamma} + c_{y} z_{20}\right) \,\mathbf{\hat{y}}- c_{z} z_{20} \,\mathbf{\hat{z}}$ | (2i) | C XX |
$\mathbf{B_{41}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $\left(a x_{21} + b y_{21} \cos{\gamma} + c_{x} z_{21}\right) \,\mathbf{\hat{x}}+\left(b y_{21} \sin{\gamma} + c_{y} z_{21}\right) \,\mathbf{\hat{y}}+c_{z} z_{21} \,\mathbf{\hat{z}}$ | (2i) | C XXI |
$\mathbf{B_{42}}$ | = | $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $- \left(a x_{21} + b y_{21} \cos{\gamma} + c_{x} z_{21}\right) \,\mathbf{\hat{x}}- \left(b y_{21} \sin{\gamma} + c_{y} z_{21}\right) \,\mathbf{\hat{y}}- c_{z} z_{21} \,\mathbf{\hat{z}}$ | (2i) | C XXI |
$\mathbf{B_{43}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $\left(a x_{22} + b y_{22} \cos{\gamma} + c_{x} z_{22}\right) \,\mathbf{\hat{x}}+\left(b y_{22} \sin{\gamma} + c_{y} z_{22}\right) \,\mathbf{\hat{y}}+c_{z} z_{22} \,\mathbf{\hat{z}}$ | (2i) | C XXII |
$\mathbf{B_{44}}$ | = | $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $- \left(a x_{22} + b y_{22} \cos{\gamma} + c_{x} z_{22}\right) \,\mathbf{\hat{x}}- \left(b y_{22} \sin{\gamma} + c_{y} z_{22}\right) \,\mathbf{\hat{y}}- c_{z} z_{22} \,\mathbf{\hat{z}}$ | (2i) | C XXII |
$\mathbf{B_{45}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $\left(a x_{23} + b y_{23} \cos{\gamma} + c_{x} z_{23}\right) \,\mathbf{\hat{x}}+\left(b y_{23} \sin{\gamma} + c_{y} z_{23}\right) \,\mathbf{\hat{y}}+c_{z} z_{23} \,\mathbf{\hat{z}}$ | (2i) | H I |
$\mathbf{B_{46}}$ | = | $- x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $- \left(a x_{23} + b y_{23} \cos{\gamma} + c_{x} z_{23}\right) \,\mathbf{\hat{x}}- \left(b y_{23} \sin{\gamma} + c_{y} z_{23}\right) \,\mathbf{\hat{y}}- c_{z} z_{23} \,\mathbf{\hat{z}}$ | (2i) | H I |
$\mathbf{B_{47}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $\left(a x_{24} + b y_{24} \cos{\gamma} + c_{x} z_{24}\right) \,\mathbf{\hat{x}}+\left(b y_{24} \sin{\gamma} + c_{y} z_{24}\right) \,\mathbf{\hat{y}}+c_{z} z_{24} \,\mathbf{\hat{z}}$ | (2i) | H II |
$\mathbf{B_{48}}$ | = | $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $- \left(a x_{24} + b y_{24} \cos{\gamma} + c_{x} z_{24}\right) \,\mathbf{\hat{x}}- \left(b y_{24} \sin{\gamma} + c_{y} z_{24}\right) \,\mathbf{\hat{y}}- c_{z} z_{24} \,\mathbf{\hat{z}}$ | (2i) | H II |
$\mathbf{B_{49}}$ | = | $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ | = | $\left(a x_{25} + b y_{25} \cos{\gamma} + c_{x} z_{25}\right) \,\mathbf{\hat{x}}+\left(b y_{25} \sin{\gamma} + c_{y} z_{25}\right) \,\mathbf{\hat{y}}+c_{z} z_{25} \,\mathbf{\hat{z}}$ | (2i) | H III |
$\mathbf{B_{50}}$ | = | $- x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}- z_{25} \, \mathbf{a}_{3}$ | = | $- \left(a x_{25} + b y_{25} \cos{\gamma} + c_{x} z_{25}\right) \,\mathbf{\hat{x}}- \left(b y_{25} \sin{\gamma} + c_{y} z_{25}\right) \,\mathbf{\hat{y}}- c_{z} z_{25} \,\mathbf{\hat{z}}$ | (2i) | H III |
$\mathbf{B_{51}}$ | = | $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ | = | $\left(a x_{26} + b y_{26} \cos{\gamma} + c_{x} z_{26}\right) \,\mathbf{\hat{x}}+\left(b y_{26} \sin{\gamma} + c_{y} z_{26}\right) \,\mathbf{\hat{y}}+c_{z} z_{26} \,\mathbf{\hat{z}}$ | (2i) | H IV |
$\mathbf{B_{52}}$ | = | $- x_{26} \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}- z_{26} \, \mathbf{a}_{3}$ | = | $- \left(a x_{26} + b y_{26} \cos{\gamma} + c_{x} z_{26}\right) \,\mathbf{\hat{x}}- \left(b y_{26} \sin{\gamma} + c_{y} z_{26}\right) \,\mathbf{\hat{y}}- c_{z} z_{26} \,\mathbf{\hat{z}}$ | (2i) | H IV |
$\mathbf{B_{53}}$ | = | $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ | = | $\left(a x_{27} + b y_{27} \cos{\gamma} + c_{x} z_{27}\right) \,\mathbf{\hat{x}}+\left(b y_{27} \sin{\gamma} + c_{y} z_{27}\right) \,\mathbf{\hat{y}}+c_{z} z_{27} \,\mathbf{\hat{z}}$ | (2i) | H V |
$\mathbf{B_{54}}$ | = | $- x_{27} \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}- z_{27} \, \mathbf{a}_{3}$ | = | $- \left(a x_{27} + b y_{27} \cos{\gamma} + c_{x} z_{27}\right) \,\mathbf{\hat{x}}- \left(b y_{27} \sin{\gamma} + c_{y} z_{27}\right) \,\mathbf{\hat{y}}- c_{z} z_{27} \,\mathbf{\hat{z}}$ | (2i) | H V |
$\mathbf{B_{55}}$ | = | $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ | = | $\left(a x_{28} + b y_{28} \cos{\gamma} + c_{x} z_{28}\right) \,\mathbf{\hat{x}}+\left(b y_{28} \sin{\gamma} + c_{y} z_{28}\right) \,\mathbf{\hat{y}}+c_{z} z_{28} \,\mathbf{\hat{z}}$ | (2i) | H VI |
$\mathbf{B_{56}}$ | = | $- x_{28} \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}- z_{28} \, \mathbf{a}_{3}$ | = | $- \left(a x_{28} + b y_{28} \cos{\gamma} + c_{x} z_{28}\right) \,\mathbf{\hat{x}}- \left(b y_{28} \sin{\gamma} + c_{y} z_{28}\right) \,\mathbf{\hat{y}}- c_{z} z_{28} \,\mathbf{\hat{z}}$ | (2i) | H VI |
$\mathbf{B_{57}}$ | = | $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ | = | $\left(a x_{29} + b y_{29} \cos{\gamma} + c_{x} z_{29}\right) \,\mathbf{\hat{x}}+\left(b y_{29} \sin{\gamma} + c_{y} z_{29}\right) \,\mathbf{\hat{y}}+c_{z} z_{29} \,\mathbf{\hat{z}}$ | (2i) | H VII |
$\mathbf{B_{58}}$ | = | $- x_{29} \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}- z_{29} \, \mathbf{a}_{3}$ | = | $- \left(a x_{29} + b y_{29} \cos{\gamma} + c_{x} z_{29}\right) \,\mathbf{\hat{x}}- \left(b y_{29} \sin{\gamma} + c_{y} z_{29}\right) \,\mathbf{\hat{y}}- c_{z} z_{29} \,\mathbf{\hat{z}}$ | (2i) | H VII |
$\mathbf{B_{59}}$ | = | $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ | = | $\left(a x_{30} + b y_{30} \cos{\gamma} + c_{x} z_{30}\right) \,\mathbf{\hat{x}}+\left(b y_{30} \sin{\gamma} + c_{y} z_{30}\right) \,\mathbf{\hat{y}}+c_{z} z_{30} \,\mathbf{\hat{z}}$ | (2i) | H VIII |
$\mathbf{B_{60}}$ | = | $- x_{30} \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}- z_{30} \, \mathbf{a}_{3}$ | = | $- \left(a x_{30} + b y_{30} \cos{\gamma} + c_{x} z_{30}\right) \,\mathbf{\hat{x}}- \left(b y_{30} \sin{\gamma} + c_{y} z_{30}\right) \,\mathbf{\hat{y}}- c_{z} z_{30} \,\mathbf{\hat{z}}$ | (2i) | H VIII |
$\mathbf{B_{61}}$ | = | $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ | = | $\left(a x_{31} + b y_{31} \cos{\gamma} + c_{x} z_{31}\right) \,\mathbf{\hat{x}}+\left(b y_{31} \sin{\gamma} + c_{y} z_{31}\right) \,\mathbf{\hat{y}}+c_{z} z_{31} \,\mathbf{\hat{z}}$ | (2i) | H IX |
$\mathbf{B_{62}}$ | = | $- x_{31} \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}- z_{31} \, \mathbf{a}_{3}$ | = | $- \left(a x_{31} + b y_{31} \cos{\gamma} + c_{x} z_{31}\right) \,\mathbf{\hat{x}}- \left(b y_{31} \sin{\gamma} + c_{y} z_{31}\right) \,\mathbf{\hat{y}}- c_{z} z_{31} \,\mathbf{\hat{z}}$ | (2i) | H IX |
$\mathbf{B_{63}}$ | = | $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ | = | $\left(a x_{32} + b y_{32} \cos{\gamma} + c_{x} z_{32}\right) \,\mathbf{\hat{x}}+\left(b y_{32} \sin{\gamma} + c_{y} z_{32}\right) \,\mathbf{\hat{y}}+c_{z} z_{32} \,\mathbf{\hat{z}}$ | (2i) | H X |
$\mathbf{B_{64}}$ | = | $- x_{32} \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}- z_{32} \, \mathbf{a}_{3}$ | = | $- \left(a x_{32} + b y_{32} \cos{\gamma} + c_{x} z_{32}\right) \,\mathbf{\hat{x}}- \left(b y_{32} \sin{\gamma} + c_{y} z_{32}\right) \,\mathbf{\hat{y}}- c_{z} z_{32} \,\mathbf{\hat{z}}$ | (2i) | H X |
$\mathbf{B_{65}}$ | = | $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ | = | $\left(a x_{33} + b y_{33} \cos{\gamma} + c_{x} z_{33}\right) \,\mathbf{\hat{x}}+\left(b y_{33} \sin{\gamma} + c_{y} z_{33}\right) \,\mathbf{\hat{y}}+c_{z} z_{33} \,\mathbf{\hat{z}}$ | (2i) | H XI |
$\mathbf{B_{66}}$ | = | $- x_{33} \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}- z_{33} \, \mathbf{a}_{3}$ | = | $- \left(a x_{33} + b y_{33} \cos{\gamma} + c_{x} z_{33}\right) \,\mathbf{\hat{x}}- \left(b y_{33} \sin{\gamma} + c_{y} z_{33}\right) \,\mathbf{\hat{y}}- c_{z} z_{33} \,\mathbf{\hat{z}}$ | (2i) | H XI |
$\mathbf{B_{67}}$ | = | $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ | = | $\left(a x_{34} + b y_{34} \cos{\gamma} + c_{x} z_{34}\right) \,\mathbf{\hat{x}}+\left(b y_{34} \sin{\gamma} + c_{y} z_{34}\right) \,\mathbf{\hat{y}}+c_{z} z_{34} \,\mathbf{\hat{z}}$ | (2i) | H XII |
$\mathbf{B_{68}}$ | = | $- x_{34} \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}- z_{34} \, \mathbf{a}_{3}$ | = | $- \left(a x_{34} + b y_{34} \cos{\gamma} + c_{x} z_{34}\right) \,\mathbf{\hat{x}}- \left(b y_{34} \sin{\gamma} + c_{y} z_{34}\right) \,\mathbf{\hat{y}}- c_{z} z_{34} \,\mathbf{\hat{z}}$ | (2i) | H XII |
$\mathbf{B_{69}}$ | = | $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ | = | $\left(a x_{35} + b y_{35} \cos{\gamma} + c_{x} z_{35}\right) \,\mathbf{\hat{x}}+\left(b y_{35} \sin{\gamma} + c_{y} z_{35}\right) \,\mathbf{\hat{y}}+c_{z} z_{35} \,\mathbf{\hat{z}}$ | (2i) | H XIII |
$\mathbf{B_{70}}$ | = | $- x_{35} \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}- z_{35} \, \mathbf{a}_{3}$ | = | $- \left(a x_{35} + b y_{35} \cos{\gamma} + c_{x} z_{35}\right) \,\mathbf{\hat{x}}- \left(b y_{35} \sin{\gamma} + c_{y} z_{35}\right) \,\mathbf{\hat{y}}- c_{z} z_{35} \,\mathbf{\hat{z}}$ | (2i) | H XIII |
$\mathbf{B_{71}}$ | = | $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ | = | $\left(a x_{36} + b y_{36} \cos{\gamma} + c_{x} z_{36}\right) \,\mathbf{\hat{x}}+\left(b y_{36} \sin{\gamma} + c_{y} z_{36}\right) \,\mathbf{\hat{y}}+c_{z} z_{36} \,\mathbf{\hat{z}}$ | (2i) | H XIV |
$\mathbf{B_{72}}$ | = | $- x_{36} \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}- z_{36} \, \mathbf{a}_{3}$ | = | $- \left(a x_{36} + b y_{36} \cos{\gamma} + c_{x} z_{36}\right) \,\mathbf{\hat{x}}- \left(b y_{36} \sin{\gamma} + c_{y} z_{36}\right) \,\mathbf{\hat{y}}- c_{z} z_{36} \,\mathbf{\hat{z}}$ | (2i) | H XIV |