Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & =& y_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& y_{1} \, b \, \mathbf{\hat{y}} + z_{1} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{As} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{1} - y_{1} \, \mathbf{a}_{2} + \left(\frac12 + z_{1}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{1} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{1}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{As} \\ \mathbf{B}_{3} & =& y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& y_{2} \, b \, \mathbf{\hat{y}} + z_{2} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Cu I} \\ \mathbf{B}_{4} & =& \frac12 \, \mathbf{a}_{1} - y_{2} \, \mathbf{a}_{2} + \left(\frac12 + z_{2}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{2} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{2}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Cu I} \\ \mathbf{B}_{5} & =& y_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& y_{3} \, b \, \mathbf{\hat{y}} + z_{3} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{S I} \\ \mathbf{B}_{6} & =& \frac12 \, \mathbf{a}_{1} - y_{3} \, \mathbf{a}_{2} + \left(\frac12 + z_{3}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{3} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{3}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{S I} \\ \mathbf{B}_{7} & =& y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& y_{4} \, b \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{S II} \\ \mathbf{B}_{8} & =& \frac12 \, \mathbf{a}_{1} - y_{4} \, \mathbf{a}_{2} + \left(\frac12 + z_{4}\right) \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - y_{4} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{4}\right) \, c \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{S II} \\ \mathbf{B}_{9} & =& x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& x_{5} \, a \, \mathbf{\hat{x}} + y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu II} \\ \mathbf{B}_{10} & =& \left(\frac12 - x_{5}\right) \, \mathbf{a}_{1} - y_{5} \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{5}\right) \, a \, \mathbf{\hat{x}} - y_{5} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu II} \\ \mathbf{B}_{11} & =& \left(\frac12 + x_{5}\right) \, \mathbf{a}_{1} - y_{5} \, \mathbf{a}_{2}+ \left(\frac12 + z_{5}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{5}\right) \, a \, \mathbf{\hat{x}} - y_{5} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{5}\right) \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu II} \\ \mathbf{B}_{12} & =& - x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& - x_{5} \, a \, \mathbf{\hat{x}} + y_{5} \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Cu II} \\ \mathbf{B}_{13} & =& x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& x_{6} \, a \, \mathbf{\hat{x}} + y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{S III} \\ \mathbf{B}_{14} & =& \left(\frac12 - x_{6}\right) \, \mathbf{a}_{1} - y_{6} \, \mathbf{a}_{2}+ \left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_{6}\right) \, a \, \mathbf{\hat{x}} - y_{6} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{S III} \\ \mathbf{B}_{15} & =& \left(\frac12 + x_{6}\right) \, \mathbf{a}_{1} - y_{6} \, \mathbf{a}_{2}+ \left(\frac12 + z_{6}\right) \, \mathbf{a}_{3}& =& \left(\frac12 + x_{6}\right) \, a \, \mathbf{\hat{x}} - y_{6} \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_{6}\right) \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{S III} \\ \mathbf{B}_{16} & =& - x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& - x_{6} \, a \, \mathbf{\hat{x}} + y_{6} \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{S III} \\ \end{array} \]