Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Th} \\ \mathbf{B}_{2} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Th} \\ \mathbf{B}_{3} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} +x_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - x_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{7} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - x_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}\right) \, \mathbf{a}_{3} & = & \left(- \frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{Cl} \\ \end{array} \]