Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A7B5C3D6_oP168_29_14a_10a_6a_12a-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.

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https://aflow.org/p/EY4Y
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Orthorhombic 2-4-6 Trinitrotoluene (C$_{7}$H$_{5}$N$_{3}$O$_{6}$) Structure: A7B5C3D6_oP168_29_14a_10a_6a_12a-001

Picture of Structure; Click for Big Picture
Prototype C$_{7}$H$_{5}$N$_{3}$O$_{6}$
AFLOW prototype label A7B5C3D6_oP168_29_14a_10a_6a_12a-001
Mineral name 2-4-6 trinitrotoluene
CCDC 227800
Pearson symbol oP168
Space group number 29
Space group symbol $Pca2_1$
AFLOW prototype command aflow --proto=A7B5C3D6_oP168_29_14a_10a_6a_12a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \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}, \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}$

  • The solid form of 2-4-6 Trinitrotoluene (TNT) has two polymorphs (Vrcelj, 2003):
  • Both can be prepared at room temperature, from ethyl acetate and ethanol solutions, respectively.
  • Data for the orthorhombic phase was taken at 123K.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ (4a) C I
$\mathbf{B_{2}}$ = $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C I
$\mathbf{B_{3}}$ = $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ = $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ (4a) C I
$\mathbf{B_{4}}$ = $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C I
$\mathbf{B_{5}}$ = $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (4a) C II
$\mathbf{B_{6}}$ = $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C II
$\mathbf{B_{7}}$ = $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ (4a) C II
$\mathbf{B_{8}}$ = $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C II
$\mathbf{B_{9}}$ = $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4a) C III
$\mathbf{B_{10}}$ = $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{3} \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C III
$\mathbf{B_{11}}$ = $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ = $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (4a) C III
$\mathbf{B_{12}}$ = $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C III
$\mathbf{B_{13}}$ = $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4a) C IV
$\mathbf{B_{14}}$ = $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C IV
$\mathbf{B_{15}}$ = $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ = $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (4a) C IV
$\mathbf{B_{16}}$ = $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C IV
$\mathbf{B_{17}}$ = $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4a) C V
$\mathbf{B_{18}}$ = $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C V
$\mathbf{B_{19}}$ = $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ = $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (4a) C V
$\mathbf{B_{20}}$ = $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C V
$\mathbf{B_{21}}$ = $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4a) C VI
$\mathbf{B_{22}}$ = $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VI
$\mathbf{B_{23}}$ = $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ = $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (4a) C VI
$\mathbf{B_{24}}$ = $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VI
$\mathbf{B_{25}}$ = $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4a) C VII
$\mathbf{B_{26}}$ = $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{7} \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VII
$\mathbf{B_{27}}$ = $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ = $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ (4a) C VII
$\mathbf{B_{28}}$ = $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VII
$\mathbf{B_{29}}$ = $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4a) C VIII
$\mathbf{B_{30}}$ = $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{8} \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VIII
$\mathbf{B_{31}}$ = $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ = $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ (4a) C VIII
$\mathbf{B_{32}}$ = $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C VIII
$\mathbf{B_{33}}$ = $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4a) C IX
$\mathbf{B_{34}}$ = $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C IX
$\mathbf{B_{35}}$ = $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ = $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ (4a) C IX
$\mathbf{B_{36}}$ = $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C IX
$\mathbf{B_{37}}$ = $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4a) C X
$\mathbf{B_{38}}$ = $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C X
$\mathbf{B_{39}}$ = $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ = $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ (4a) C X
$\mathbf{B_{40}}$ = $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C X
$\mathbf{B_{41}}$ = $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4a) C XI
$\mathbf{B_{42}}$ = $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XI
$\mathbf{B_{43}}$ = $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ = $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ (4a) C XI
$\mathbf{B_{44}}$ = $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XI
$\mathbf{B_{45}}$ = $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4a) C XII
$\mathbf{B_{46}}$ = $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{12} \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XII
$\mathbf{B_{47}}$ = $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ = $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ (4a) C XII
$\mathbf{B_{48}}$ = $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XII
$\mathbf{B_{49}}$ = $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4a) C XIII
$\mathbf{B_{50}}$ = $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{13} \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XIII
$\mathbf{B_{51}}$ = $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ = $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ (4a) C XIII
$\mathbf{B_{52}}$ = $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XIII
$\mathbf{B_{53}}$ = $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4a) C XIV
$\mathbf{B_{54}}$ = $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{14} \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XIV
$\mathbf{B_{55}}$ = $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ = $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ (4a) C XIV
$\mathbf{B_{56}}$ = $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) C XIV
$\mathbf{B_{57}}$ = $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4a) H I
$\mathbf{B_{58}}$ = $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{15} \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H I
$\mathbf{B_{59}}$ = $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ = $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ (4a) H I
$\mathbf{B_{60}}$ = $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H I
$\mathbf{B_{61}}$ = $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4a) H II
$\mathbf{B_{62}}$ = $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{16} \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H II
$\mathbf{B_{63}}$ = $\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ = $a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ (4a) H II
$\mathbf{B_{64}}$ = $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H II
$\mathbf{B_{65}}$ = $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4a) H III
$\mathbf{B_{66}}$ = $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{17} \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H III
$\mathbf{B_{67}}$ = $\left(x_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ = $a \left(x_{17} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ (4a) H III
$\mathbf{B_{68}}$ = $- \left(x_{17} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{17} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H III
$\mathbf{B_{69}}$ = $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a x_{18} \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4a) H IV
$\mathbf{B_{70}}$ = $- x_{18} \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{18} \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H IV
$\mathbf{B_{71}}$ = $\left(x_{18} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ = $a \left(x_{18} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ (4a) H IV
$\mathbf{B_{72}}$ = $- \left(x_{18} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{18} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H IV
$\mathbf{B_{73}}$ = $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4a) H V
$\mathbf{B_{74}}$ = $- x_{19} \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{19} \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H V
$\mathbf{B_{75}}$ = $\left(x_{19} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ = $a \left(x_{19} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ (4a) H V
$\mathbf{B_{76}}$ = $- \left(x_{19} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{19} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H V
$\mathbf{B_{77}}$ = $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4a) H VI
$\mathbf{B_{78}}$ = $- x_{20} \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{20} \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VI
$\mathbf{B_{79}}$ = $\left(x_{20} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ = $a \left(x_{20} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ (4a) H VI
$\mathbf{B_{80}}$ = $- \left(x_{20} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{20} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VI
$\mathbf{B_{81}}$ = $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4a) H VII
$\mathbf{B_{82}}$ = $- x_{21} \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{21} \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VII
$\mathbf{B_{83}}$ = $\left(x_{21} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ = $a \left(x_{21} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ (4a) H VII
$\mathbf{B_{84}}$ = $- \left(x_{21} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{21} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VII
$\mathbf{B_{85}}$ = $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4a) H VIII
$\mathbf{B_{86}}$ = $- x_{22} \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{22} \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VIII
$\mathbf{B_{87}}$ = $\left(x_{22} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ = $a \left(x_{22} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ (4a) H VIII
$\mathbf{B_{88}}$ = $- \left(x_{22} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{22} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H VIII
$\mathbf{B_{89}}$ = $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4a) H IX
$\mathbf{B_{90}}$ = $- x_{23} \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{23} \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H IX
$\mathbf{B_{91}}$ = $\left(x_{23} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ = $a \left(x_{23} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ (4a) H IX
$\mathbf{B_{92}}$ = $- \left(x_{23} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{23} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H IX
$\mathbf{B_{93}}$ = $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4a) H X
$\mathbf{B_{94}}$ = $- x_{24} \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{24} \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H X
$\mathbf{B_{95}}$ = $\left(x_{24} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ = $a \left(x_{24} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ (4a) H X
$\mathbf{B_{96}}$ = $- \left(x_{24} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{24} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) H X
$\mathbf{B_{97}}$ = $x_{25} \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ = $a x_{25} \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ (4a) N I
$\mathbf{B_{98}}$ = $- x_{25} \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{25} \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N I
$\mathbf{B_{99}}$ = $\left(x_{25} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{25} \, \mathbf{a}_{2}+z_{25} \, \mathbf{a}_{3}$ = $a \left(x_{25} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{25} \,\mathbf{\hat{y}}+c z_{25} \,\mathbf{\hat{z}}$ (4a) N I
$\mathbf{B_{100}}$ = $- \left(x_{25} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{25} \, \mathbf{a}_{2}+\left(z_{25} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{25} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{25} \,\mathbf{\hat{y}}+c \left(z_{25} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N I
$\mathbf{B_{101}}$ = $x_{26} \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ = $a x_{26} \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ (4a) N II
$\mathbf{B_{102}}$ = $- x_{26} \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{26} \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N II
$\mathbf{B_{103}}$ = $\left(x_{26} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{26} \, \mathbf{a}_{2}+z_{26} \, \mathbf{a}_{3}$ = $a \left(x_{26} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{26} \,\mathbf{\hat{y}}+c z_{26} \,\mathbf{\hat{z}}$ (4a) N II
$\mathbf{B_{104}}$ = $- \left(x_{26} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{26} \, \mathbf{a}_{2}+\left(z_{26} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{26} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{26} \,\mathbf{\hat{y}}+c \left(z_{26} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N II
$\mathbf{B_{105}}$ = $x_{27} \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ = $a x_{27} \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ (4a) N III
$\mathbf{B_{106}}$ = $- x_{27} \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{27} \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N III
$\mathbf{B_{107}}$ = $\left(x_{27} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{27} \, \mathbf{a}_{2}+z_{27} \, \mathbf{a}_{3}$ = $a \left(x_{27} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{27} \,\mathbf{\hat{y}}+c z_{27} \,\mathbf{\hat{z}}$ (4a) N III
$\mathbf{B_{108}}$ = $- \left(x_{27} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{27} \, \mathbf{a}_{2}+\left(z_{27} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{27} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{27} \,\mathbf{\hat{y}}+c \left(z_{27} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N III
$\mathbf{B_{109}}$ = $x_{28} \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ = $a x_{28} \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ (4a) N IV
$\mathbf{B_{110}}$ = $- x_{28} \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{28} \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N IV
$\mathbf{B_{111}}$ = $\left(x_{28} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{28} \, \mathbf{a}_{2}+z_{28} \, \mathbf{a}_{3}$ = $a \left(x_{28} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{28} \,\mathbf{\hat{y}}+c z_{28} \,\mathbf{\hat{z}}$ (4a) N IV
$\mathbf{B_{112}}$ = $- \left(x_{28} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{28} \, \mathbf{a}_{2}+\left(z_{28} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{28} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{28} \,\mathbf{\hat{y}}+c \left(z_{28} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N IV
$\mathbf{B_{113}}$ = $x_{29} \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ = $a x_{29} \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c z_{29} \,\mathbf{\hat{z}}$ (4a) N V
$\mathbf{B_{114}}$ = $- x_{29} \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}+\left(z_{29} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{29} \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c \left(z_{29} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N V
$\mathbf{B_{115}}$ = $\left(x_{29} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{29} \, \mathbf{a}_{2}+z_{29} \, \mathbf{a}_{3}$ = $a \left(x_{29} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{29} \,\mathbf{\hat{y}}+c z_{29} \,\mathbf{\hat{z}}$ (4a) N V
$\mathbf{B_{116}}$ = $- \left(x_{29} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{29} \, \mathbf{a}_{2}+\left(z_{29} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{29} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{29} \,\mathbf{\hat{y}}+c \left(z_{29} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N V
$\mathbf{B_{117}}$ = $x_{30} \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ = $a x_{30} \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c z_{30} \,\mathbf{\hat{z}}$ (4a) N VI
$\mathbf{B_{118}}$ = $- x_{30} \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}+\left(z_{30} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{30} \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c \left(z_{30} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N VI
$\mathbf{B_{119}}$ = $\left(x_{30} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{30} \, \mathbf{a}_{2}+z_{30} \, \mathbf{a}_{3}$ = $a \left(x_{30} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{30} \,\mathbf{\hat{y}}+c z_{30} \,\mathbf{\hat{z}}$ (4a) N VI
$\mathbf{B_{120}}$ = $- \left(x_{30} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{30} \, \mathbf{a}_{2}+\left(z_{30} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{30} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{30} \,\mathbf{\hat{y}}+c \left(z_{30} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) N VI
$\mathbf{B_{121}}$ = $x_{31} \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ = $a x_{31} \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{122}}$ = $- x_{31} \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}+\left(z_{31} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{31} \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c \left(z_{31} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{123}}$ = $\left(x_{31} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{31} \, \mathbf{a}_{2}+z_{31} \, \mathbf{a}_{3}$ = $a \left(x_{31} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{31} \,\mathbf{\hat{y}}+c z_{31} \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{124}}$ = $- \left(x_{31} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{31} \, \mathbf{a}_{2}+\left(z_{31} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{31} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{31} \,\mathbf{\hat{y}}+c \left(z_{31} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O I
$\mathbf{B_{125}}$ = $x_{32} \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ = $a x_{32} \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{126}}$ = $- x_{32} \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}+\left(z_{32} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{32} \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c \left(z_{32} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{127}}$ = $\left(x_{32} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{32} \, \mathbf{a}_{2}+z_{32} \, \mathbf{a}_{3}$ = $a \left(x_{32} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{32} \,\mathbf{\hat{y}}+c z_{32} \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{128}}$ = $- \left(x_{32} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{32} \, \mathbf{a}_{2}+\left(z_{32} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{32} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{32} \,\mathbf{\hat{y}}+c \left(z_{32} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O II
$\mathbf{B_{129}}$ = $x_{33} \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ = $a x_{33} \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{130}}$ = $- x_{33} \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}+\left(z_{33} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{33} \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c \left(z_{33} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{131}}$ = $\left(x_{33} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{33} \, \mathbf{a}_{2}+z_{33} \, \mathbf{a}_{3}$ = $a \left(x_{33} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{33} \,\mathbf{\hat{y}}+c z_{33} \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{132}}$ = $- \left(x_{33} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{33} \, \mathbf{a}_{2}+\left(z_{33} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{33} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{33} \,\mathbf{\hat{y}}+c \left(z_{33} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O III
$\mathbf{B_{133}}$ = $x_{34} \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ = $a x_{34} \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{134}}$ = $- x_{34} \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}+\left(z_{34} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{34} \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c \left(z_{34} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{135}}$ = $\left(x_{34} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{34} \, \mathbf{a}_{2}+z_{34} \, \mathbf{a}_{3}$ = $a \left(x_{34} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{34} \,\mathbf{\hat{y}}+c z_{34} \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{136}}$ = $- \left(x_{34} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{34} \, \mathbf{a}_{2}+\left(z_{34} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{34} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{34} \,\mathbf{\hat{y}}+c \left(z_{34} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IV
$\mathbf{B_{137}}$ = $x_{35} \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ = $a x_{35} \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{138}}$ = $- x_{35} \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}+\left(z_{35} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{35} \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c \left(z_{35} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{139}}$ = $\left(x_{35} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{35} \, \mathbf{a}_{2}+z_{35} \, \mathbf{a}_{3}$ = $a \left(x_{35} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{35} \,\mathbf{\hat{y}}+c z_{35} \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{140}}$ = $- \left(x_{35} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{35} \, \mathbf{a}_{2}+\left(z_{35} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{35} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{35} \,\mathbf{\hat{y}}+c \left(z_{35} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O V
$\mathbf{B_{141}}$ = $x_{36} \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ = $a x_{36} \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{142}}$ = $- x_{36} \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}+\left(z_{36} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{36} \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c \left(z_{36} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{143}}$ = $\left(x_{36} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{36} \, \mathbf{a}_{2}+z_{36} \, \mathbf{a}_{3}$ = $a \left(x_{36} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{36} \,\mathbf{\hat{y}}+c z_{36} \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{144}}$ = $- \left(x_{36} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{36} \, \mathbf{a}_{2}+\left(z_{36} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{36} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{36} \,\mathbf{\hat{y}}+c \left(z_{36} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VI
$\mathbf{B_{145}}$ = $x_{37} \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ = $a x_{37} \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{146}}$ = $- x_{37} \, \mathbf{a}_{1}- y_{37} \, \mathbf{a}_{2}+\left(z_{37} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{37} \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c \left(z_{37} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{147}}$ = $\left(x_{37} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{37} \, \mathbf{a}_{2}+z_{37} \, \mathbf{a}_{3}$ = $a \left(x_{37} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{37} \,\mathbf{\hat{y}}+c z_{37} \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{148}}$ = $- \left(x_{37} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{37} \, \mathbf{a}_{2}+\left(z_{37} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{37} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{37} \,\mathbf{\hat{y}}+c \left(z_{37} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VII
$\mathbf{B_{149}}$ = $x_{38} \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ = $a x_{38} \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{150}}$ = $- x_{38} \, \mathbf{a}_{1}- y_{38} \, \mathbf{a}_{2}+\left(z_{38} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{38} \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c \left(z_{38} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{151}}$ = $\left(x_{38} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{38} \, \mathbf{a}_{2}+z_{38} \, \mathbf{a}_{3}$ = $a \left(x_{38} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{38} \,\mathbf{\hat{y}}+c z_{38} \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{152}}$ = $- \left(x_{38} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{38} \, \mathbf{a}_{2}+\left(z_{38} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{38} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{38} \,\mathbf{\hat{y}}+c \left(z_{38} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O VIII
$\mathbf{B_{153}}$ = $x_{39} \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ = $a x_{39} \,\mathbf{\hat{x}}+b y_{39} \,\mathbf{\hat{y}}+c z_{39} \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{154}}$ = $- x_{39} \, \mathbf{a}_{1}- y_{39} \, \mathbf{a}_{2}+\left(z_{39} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{39} \,\mathbf{\hat{x}}- b y_{39} \,\mathbf{\hat{y}}+c \left(z_{39} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{155}}$ = $\left(x_{39} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{39} \, \mathbf{a}_{2}+z_{39} \, \mathbf{a}_{3}$ = $a \left(x_{39} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{39} \,\mathbf{\hat{y}}+c z_{39} \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{156}}$ = $- \left(x_{39} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{39} \, \mathbf{a}_{2}+\left(z_{39} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{39} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{39} \,\mathbf{\hat{y}}+c \left(z_{39} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O IX
$\mathbf{B_{157}}$ = $x_{40} \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ = $a x_{40} \,\mathbf{\hat{x}}+b y_{40} \,\mathbf{\hat{y}}+c z_{40} \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{158}}$ = $- x_{40} \, \mathbf{a}_{1}- y_{40} \, \mathbf{a}_{2}+\left(z_{40} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{40} \,\mathbf{\hat{x}}- b y_{40} \,\mathbf{\hat{y}}+c \left(z_{40} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{159}}$ = $\left(x_{40} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{40} \, \mathbf{a}_{2}+z_{40} \, \mathbf{a}_{3}$ = $a \left(x_{40} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{40} \,\mathbf{\hat{y}}+c z_{40} \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{160}}$ = $- \left(x_{40} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{40} \, \mathbf{a}_{2}+\left(z_{40} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{40} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{40} \,\mathbf{\hat{y}}+c \left(z_{40} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O X
$\mathbf{B_{161}}$ = $x_{41} \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}+z_{41} \, \mathbf{a}_{3}$ = $a x_{41} \,\mathbf{\hat{x}}+b y_{41} \,\mathbf{\hat{y}}+c z_{41} \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{162}}$ = $- x_{41} \, \mathbf{a}_{1}- y_{41} \, \mathbf{a}_{2}+\left(z_{41} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{41} \,\mathbf{\hat{x}}- b y_{41} \,\mathbf{\hat{y}}+c \left(z_{41} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{163}}$ = $\left(x_{41} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{41} \, \mathbf{a}_{2}+z_{41} \, \mathbf{a}_{3}$ = $a \left(x_{41} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{41} \,\mathbf{\hat{y}}+c z_{41} \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{164}}$ = $- \left(x_{41} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{41} \, \mathbf{a}_{2}+\left(z_{41} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{41} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{41} \,\mathbf{\hat{y}}+c \left(z_{41} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XI
$\mathbf{B_{165}}$ = $x_{42} \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}+z_{42} \, \mathbf{a}_{3}$ = $a x_{42} \,\mathbf{\hat{x}}+b y_{42} \,\mathbf{\hat{y}}+c z_{42} \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{166}}$ = $- x_{42} \, \mathbf{a}_{1}- y_{42} \, \mathbf{a}_{2}+\left(z_{42} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{42} \,\mathbf{\hat{x}}- b y_{42} \,\mathbf{\hat{y}}+c \left(z_{42} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{167}}$ = $\left(x_{42} + \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{42} \, \mathbf{a}_{2}+z_{42} \, \mathbf{a}_{3}$ = $a \left(x_{42} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{42} \,\mathbf{\hat{y}}+c z_{42} \,\mathbf{\hat{z}}$ (4a) O XII
$\mathbf{B_{168}}$ = $- \left(x_{42} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{42} \, \mathbf{a}_{2}+\left(z_{42} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{42} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+b y_{42} \,\mathbf{\hat{y}}+c \left(z_{42} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ (4a) O XII

References

  • R. M. Vrcelj, J. N. Sherwood, A. R. Kennedy, H. G. Gallagher, and T. Gelbrich, Polymorphism in 2-4-6 Trinitrotoluene, Crystal Growth & Design 3, 1027–1032 (2003), doi:10.1021/cg0340704.

Prototype Generator

aflow --proto=A7B5C3D6_oP168_29_14a_10a_6a_12a --params=$a,b/a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24},x_{25},y_{25},z_{25},x_{26},y_{26},z_{26},x_{27},y_{27},z_{27},x_{28},y_{28},z_{28},x_{29},y_{29},z_{29},x_{30},y_{30},z_{30},x_{31},y_{31},z_{31},x_{32},y_{32},z_{32},x_{33},y_{33},z_{33},x_{34},y_{34},z_{34},x_{35},y_{35},z_{35},x_{36},y_{36},z_{36},x_{37},y_{37},z_{37},x_{38},y_{38},z_{38},x_{39},y_{39},z_{39},x_{40},y_{40},z_{40},x_{41},y_{41},z_{41},x_{42},y_{42},z_{42}$

Species:

Running:

Output: