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} + \frac14 \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3}& =& \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu I} \\ \mathbf{B}_{2} & =& - x_{1} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{1} \, \mathbf{a}_{3}& =& - \left(x_{1} \, a + z_{1} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{1} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu I} \\ \mathbf{B}_{3} & =& x_{2} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3}& =& \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu II} \\ \mathbf{B}_{4} & =& - x_{2} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{2} \, \mathbf{a}_{3}& =& - \left(x_{2} \, a + z_{2} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{2} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu II} \\ \mathbf{B}_{5} & =& x_{3} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3}& =& \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu III} \\ \mathbf{B}_{6} & =& - x_{3} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{3} \, \mathbf{a}_{3}& =& - \left(x_{3} \, a + z_{3} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{3} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu III} \\ \mathbf{B}_{7} & =& x_{4} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3}& =& \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu IV} \\ \mathbf{B}_{8} & =& - x_{4} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{4} \, \mathbf{a}_{3}& =& - \left(x_{4} \, a + z_{4} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{4} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu IV} \\ \mathbf{B}_{9} & =& x_{5} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3}& =& \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu V} \\ \mathbf{B}_{10} & =& - x_{5} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{5} \, \mathbf{a}_{3}& =& - \left(x_{5} \, a + z_{5} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{5} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu V} \\ \mathbf{B}_{11} & =& x_{6} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VI} \\ \mathbf{B}_{12} & =& - x_{6} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& - \left(x_{6} \, a + z_{6} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{6} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VI} \\ \mathbf{B}_{13} & =& x_{7} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3}& =& \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VII} \\ \mathbf{B}_{14} & =& - x_{7} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{7} \, \mathbf{a}_{3}& =& - \left(x_{7} \, a + z_{7} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{7} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VII} \\ \mathbf{B}_{15} & =& x_{8} \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& \left(x_{8} \, a + z_{8} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac14 \, b \, \mathbf{\hat{y}}+ z_{8} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VIII} \\ \mathbf{B}_{16} & =& - x_{8} \, \mathbf{a}_{1} + \frac34 \, \mathbf{a}_{2} - z_{8} \, \mathbf{a}_{3}& =& - \left(x_{8} \, a + z_{8} \, c \, \cos\beta\right) \, \mathbf{\hat{x}}+ \frac34 \, b \, \mathbf{\hat{y}}- z_{8} \, c \, \sin\beta \, \mathbf{\hat{z}}& \left(2e\right) & \mbox{Pu VIII} \\ \end{array} \]