Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{W} \\ \mathbf{B}_{2} & = &\left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{3} & = &\left(z_{2} - y_{2}\right) \, \mathbf{a}_{1}+ z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{y}}+ z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{4} & = &\left(y_{2} - z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+ y_{2} \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{y}}- z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{5} & = &- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{y}}- z_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{6} & = &y_{2} \, \mathbf{a}_{1}+ \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &z_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{7} & = &- y_{2} \, \mathbf{a}_{1}+ \left(z_{2} - y_{2}\right) \, \mathbf{a}_{2}+ z_{2} \, \mathbf{a}_{3}& = &z_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{8} & = &y_{2} \, \mathbf{a}_{1}+ \left(y_{2} - z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &- z_{2} \, a \, \mathbf{\hat{x}}+ y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{9} & = &- y_{2} \, \mathbf{a}_{1}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}& = &- z_{2} \, a \, \mathbf{\hat{x}}- y_{2} \, a \, \mathbf{\hat{z}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{10} & = &z_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{x}}+ z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{11} & = &z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+ \left(z_{2} - y_{2}\right) \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}+ z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{12} & = &- z_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{2}+ \left(y_{2} - z_{2}\right) \, \mathbf{a}_{3}& = &y_{2} \, a \, \mathbf{\hat{x}}- z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Al} \\ \mathbf{B}_{13} & = &- z_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- \left(y_{2} + z_{2}\right) \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}- z_{2} \, a \, \mathbf{\hat{y}}& \left(24g\right) & \mbox{Al} \\ \end{array} \]