Encyclopedia of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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(4a\right) & \text{Co} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{K I} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{K II} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \text{K II} \\ \mathbf{B}_{5} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{6} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{y}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{8} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{y}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{z}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{10} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{z}} & \left(24e\right) & \text{N} \\ \mathbf{B}_{11} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{12} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{13} & = & \left(y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{14} & = & \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{15} & = & \left(y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{16} & = & \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{17} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{18} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{z}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{19} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{20} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{21} & = & \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} & \left(48h\right) & \text{O} \\ \mathbf{B}_{22} & = & \left(y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} & \left(48h\right) & \text{O} \\ \end{array} \]