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}a \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-y_{1} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-y_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C I} \\ \mathbf{B}_{3} & = & -y_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{3} & = & -y_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C I} \\ \mathbf{B}_{4} & = & y_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{1}\right) \, \mathbf{a}_{3} & = & y_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{1}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C 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}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C II} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C II} \\ \mathbf{B}_{7} & = & -y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C II} \\ \mathbf{B}_{8} & = & y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{C 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}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{La} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-y_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{La} \\ \mathbf{B}_{11} & = & -y_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{La} \\ \mathbf{B}_{12} & = & y_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{La} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rh} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rh} \\ \mathbf{B}_{15} & = & -y_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{4}\right) \, \mathbf{a}_{3} & = & -y_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rh} \\ \mathbf{B}_{16} & = & y_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{4}\right) \, \mathbf{a}_{3} & = & y_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Rh} \\ \end{array} \]