Library of Crystallographic Prototypes

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &2 x_{1} \, \mathbf{a}_{1}+ 2 x_{1} \, \mathbf{a}_{2}+ 2 x_{1} \, \mathbf{a}_{3}& = &x_{1} \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}+ \left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{3}& = &- x_{1} \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ x_{1} \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{3} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ x_{1} \, a \, \mathbf{\hat{y}}- x_{1} \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{4} & = &\left(\frac12 - 2 x_{1}\right) \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &+ x_{1} \, a \, \mathbf{\hat{x}}- x_{1} \, a \, \mathbf{\hat{y}}\left(\frac12 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{5} & = &\left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{1}+ \left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{2}+ \left(\frac12 + 2 x_{1}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}- 2 x_{1} \, \mathbf{a}_{3}& = &\left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{7} & = &- 2 x_{1} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{8} & = &- 2 x_{1} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\left(\frac14 - x_{1}\right) \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{1}\right) \, a \, \mathbf{\hat{y}}+ \left(\frac34 - x_{1}\right) \, a \, \mathbf{\hat{z}}& \left(16c\right) & \mbox{Pu} \\ \mathbf{B}_{9} & = &\frac14 \, \mathbf{a}_{1}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{10} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{11} & = &x_{2} \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \left(\frac14 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ x_{2} \, a \, \mathbf{\hat{y}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{12} & = &\left(\frac12 - x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac14 - x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}- x_{2} \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{13} & = &\left(\frac14 + x_{2}\right) \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{y}}+ x_{2} \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{14} & = &\left(\frac14 - x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac12 - x_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}- x_{2} \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{15} & = &\left(\frac34 + x_{2}\right) \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{16} & = &\left(\frac34 - x_{2}\right) \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{17} & = &\frac34 \, \mathbf{a}_{1}+ \left(\frac12 + x_{2}\right) \, \mathbf{a}_{2}+ \left(\frac34 + x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{18} & = &\frac14 \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{3}& = &\left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{19} & = &\left(\frac12 + x_{2}\right) \, \mathbf{a}_{1}+ \left(\frac34 + x_{2}\right) \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \left(\frac14 + x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \mathbf{B}_{20} & = &- x_{2} \, \mathbf{a}_{1}+ \left(\frac34 - x_{2}\right) \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \left(\frac14 - x_{2}\right) \, a \, \mathbf{\hat{z}}& \left(24d\right) & \mbox{C} \\ \end{array} \]