Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \left(\frac{1}{4} +z_{1}\right) \, \mathbf{a}_{1} + z_{1} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{2} & = & \left(\frac{3}{4} - z_{1}\right) \, \mathbf{a}_{1}-z_{1} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{1}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{K} \\ \mathbf{B}_{3} & = & \left(y_{2}+z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + y_{2} \, \mathbf{a}_{3} & = & y_{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Hg} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Hg} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} +y_{2} - z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Hg} \\ \mathbf{B}_{6} & = & \left(-y_{2}-z_{2}\right) \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2}-y_{2} \, \mathbf{a}_{3} & = & -y_{2}b \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{Hg} \\ \end{array} \]