Library of Crystallographic Prototypes

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} + y_1 \, \mathbf{a}_{2} + z_1 \, \mathbf{a}_{3}& =& x_1 \, a \, \mathbf{\hat{x}}+ y_1 \, b \, \mathbf{\hat{y}}+ z_1 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag I} \\ \mathbf{B_2} & =& \left(\frac12 - x_1\right) \, \mathbf{a}_{1} - y_1 \, \mathbf{a}_{2} + \left(\frac12 + z_1\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_1\right) \, a \, \mathbf{\hat{x}}- y_1 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_1\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag I} \\ \mathbf{B_3} & =& - x_1 \, \mathbf{a}_{1} + \left(\frac12 + y_1\right) \, \mathbf{a}_{2} + \left(\frac12 -z_1\right) \, \mathbf{a}_{3}& =& - x_1 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_1\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_1\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag I} \\ \mathbf{B_4} & =& \left(\frac12 + x_1\right) \, \mathbf{a}_{1} + \left(\frac12 - y_1\right) \, \mathbf{a}_{2} - z_1 \, \mathbf{a}_{3}& =& \left(\frac12 + x_1\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_1\right) \, b \, \mathbf{\hat{y}}- z_1 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag I} \\ \mathbf{B_5} & =& x_2 \, \mathbf{a}_{1} + y_2 \, \mathbf{a}_{2} + z_2 \, \mathbf{a}_{3}& =& x_2 \, a \, \mathbf{\hat{x}}+ y_2 \, b \, \mathbf{\hat{y}}+ z_2 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag II} \\ \mathbf{B_6} & =& \left(\frac12 - x_2\right) \, \mathbf{a}_{1} - y_2 \, \mathbf{a}_{2} + \left(\frac12 + z_2\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_2\right) \, a \, \mathbf{\hat{x}}- y_2 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_2\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag II} \\ \mathbf{B_7} & =& - x_2 \, \mathbf{a}_{1} + \left(\frac12 + y_2\right) \, \mathbf{a}_{2} + \left(\frac12 -z_2\right) \, \mathbf{a}_{3}& =& - x_2 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_2\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_2\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag II} \\ \mathbf{B_8} & =& \left(\frac12 + x_2\right) \, \mathbf{a}_{1} + \left(\frac12 - y_2\right) \, \mathbf{a}_{2} - z_2 \, \mathbf{a}_{3}& =& \left(\frac12 + x_2\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_2\right) \, b \, \mathbf{\hat{y}}- z_2 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Ag II} \\ \mathbf{B_9} & =& x_3 \, \mathbf{a}_{1} + y_3 \, \mathbf{a}_{2} + z_3 \, \mathbf{a}_{3}& =& x_3 \, a \, \mathbf{\hat{x}}+ y_3 \, b \, \mathbf{\hat{y}}+ z_3 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Se} \\ \mathbf{B}_{10} & =& \left(\frac12 - x_3\right) \, \mathbf{a}_{1} - y_3 \, \mathbf{a}_{2} + \left(\frac12 + z_3\right) \, \mathbf{a}_{3}& =& \left(\frac12 - x_3\right) \, a \, \mathbf{\hat{x}}- y_3 \, b \, \mathbf{\hat{y}}+ \left(\frac12 + z_3\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Se} \\ \mathbf{B}_{11} & =& - x_3 \, \mathbf{a}_{1} + \left(\frac12 + y_3\right) \, \mathbf{a}_{2} + \left(\frac12 -z_3\right) \, \mathbf{a}_{3}& =& - x_3 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + y_3\right) \, b \, \mathbf{\hat{y}}+ \left(\frac12 - z_3\right) \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Se} \\ \mathbf{B}_{12} & =& \left(\frac12 + x_3\right) \, \mathbf{a}_{1} + \left(\frac12 - y_3\right) \, \mathbf{a}_{2} - z_3 \, \mathbf{a}_{3}& =& \left(\frac12 + x_3\right) \, a \, \mathbf{\hat{x}}+ \left(\frac12 - y_3\right) \, b \, \mathbf{\hat{y}}- z_3 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Se} \\ \end{array} \]