Mo4P3 Structure : A4B3_oP56_62_8c_6c

Picture of Structure; Click for Big Picture
Prototype : Mo4P3
AFLOW prototype label : A4B3_oP56_62_8c_6c
Strukturbericht designation : None
Pearson symbol : oP56
Space group number : 62
Space group symbol : $Pnma$
AFLOW prototype command : aflow --proto=A4B3_oP56_62_8c_6c
--params=
$a$,$b/a$,$c/a$,$x_{1}$,$z_{1}$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$,$x_{12}$,$z_{12}$,$x_{13}$,$z_{13}$,$x_{14}$,$z_{14}$


Simple Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo I} \\ \mathbf{B}_{2} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo I} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo I} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{1}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{1}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo I} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo II} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo II} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo II} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo II} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo III} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo III} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo III} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo III} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo IV} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo IV} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo IV} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo IV} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo V} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo V} \\ \mathbf{B}_{19} & = & -x_{5} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo V} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo V} \\ \mathbf{B}_{21} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VI} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VI} \\ \mathbf{B}_{23} & = & -x_{6} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VI} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VI} \\ \mathbf{B}_{25} & = & x_{7} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VII} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VII} \\ \mathbf{B}_{27} & = & -x_{7} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VII} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VII} \\ \mathbf{B}_{29} & = & x_{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VIII} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VIII} \\ \mathbf{B}_{31} & = & -x_{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VIII} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{Mo VIII} \\ \mathbf{B}_{33} & = & x_{9} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P I} \\ \mathbf{B}_{34} & = & \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{9}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P I} \\ \mathbf{B}_{35} & = & -x_{9} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P I} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{9}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P I} \\ \mathbf{B}_{37} & = & x_{10} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P II} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} - x_{10}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{10}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{10}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P II} \\ \mathbf{B}_{39} & = & -x_{10} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} +x_{10}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{10}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{10}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P II} \\ \mathbf{B}_{41} & = & x_{11} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P III} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} - x_{11}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{11}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{11}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P III} \\ \mathbf{B}_{43} & = & -x_{11} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{11}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P III} \\ \mathbf{B}_{44} & = & \left(\frac{1}{2} +x_{11}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{11}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{11}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P III} \\ \mathbf{B}_{45} & = & x_{12} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{12} \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P IV} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} - x_{12}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{12}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{12}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P IV} \\ \mathbf{B}_{47} & = & -x_{12} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{12} \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{12}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P IV} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} +x_{12}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{12}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{12}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P IV} \\ \mathbf{B}_{49} & = & x_{13} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{13} \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P V} \\ \mathbf{B}_{50} & = & \left(\frac{1}{2} - x_{13}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{13}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{13}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P V} \\ \mathbf{B}_{51} & = & -x_{13} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{13} \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{13}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P V} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} +x_{13}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{13}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{13}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P V} \\ \mathbf{B}_{53} & = & x_{14} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{14} \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P VI} \\ \mathbf{B}_{54} & = & \left(\frac{1}{2} - x_{14}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{14}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{14}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P VI} \\ \mathbf{B}_{55} & = & -x_{14} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{14} \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{14}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P VI} \\ \mathbf{B}_{56} & = & \left(\frac{1}{2} +x_{14}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{14}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{14}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{P VI} \\ \end{array} \]

References

Geometry files


Prototype Generator

aflow --proto=A4B3_oP56_62_8c_6c --params=

Species:

Running:

Output: