H3PW12O40·29H2O ($H4_{21}$) Structure : A29B40CD12_cF656_227_ae2fg_e3g_b_g

Picture of Structure; Click for Big Picture
Prototype : (H2O)29O40PW12
AFLOW prototype label : A29B40CD12_cF656_227_ae2fg_e3g_b_g
Strukturbericht designation : $H4_{21}$
Pearson symbol : cF656
Space group number : 227
Space group symbol : $Fd\bar{3}m$
AFLOW prototype command : aflow --proto=A29B40CD12_cF656_227_ae2fg_e3g_b_g
--params=
$a$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$,$x_{9}$,$z_{9}$,$x_{10}$,$z_{10}$,$x_{11}$,$z_{11}$


Other compounds with this structure

  • H3PMo12O40·30H2O

  • This compound is often colloquially called PWA–29. On heating some water molecules will disassociate, leaving H3PW12O40·6H2O, H3PW12O40·5H2O ($H4_{16}$), or H3PW12O40·3H2O.
  • The three hydrogen atoms not formally associated with the water molecules are not located. Presumably they join with some water molecules to form H3O+ ions.
  • Even the exact number and position of the water molecules is uncertain. (Clark, 1976), studying the related compound H3PMo12O40·30H2O, states the the composition is approximately 30H2O, and that only six of the water molecules occupy ordered sites.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{3} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{P} \\ \mathbf{B}_{4} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{5}{8}a \, \mathbf{\hat{x}} + \frac{5}{8}a \, \mathbf{\hat{y}} + \frac{5}{8}a \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{P} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{9} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{17} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{18} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{19} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{21} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{22} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{23} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{24} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{26} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{27} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{28} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{29} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{30} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{31} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{32} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O III} \\ \mathbf{B}_{33} & = & \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{34} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{35} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{36} & = & \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{37} & = & x_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{38} & = & \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{39} & = & \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{6}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{40} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{41} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{6}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{42} & = & \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{43} & = & -x_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{44} & = & \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{H$_{2}$O IV} \\ \mathbf{B}_{45} & = & z_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{46} & = & z_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{47} & = & \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{1} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{49} & = & \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{50} & = & \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{51} & = & z_{7} \, \mathbf{a}_{1} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{52} & = & z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{2} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{53} & = & z_{7} \, \mathbf{a}_{1} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{54} & = & z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{55} & = & \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{56} & = & \left(2x_{7}-z_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{7} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{7}\right)a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{57} & = & -z_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{58} & = & -z_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{59} & = & \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{60} & = & \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{1} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{61} & = & \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{62} & = & \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{63} & = & -z_{7} \, \mathbf{a}_{1} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{64} & = & -z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{65} & = & -z_{7} \, \mathbf{a}_{1} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{66} & = & -z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{2} + \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{67} & = & \left(\frac{1}{2} +2x_{7} + z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{68} & = & \left(-2x_{7}+z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{H$_{2}$O V} \\ \mathbf{B}_{69} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{70} & = & z_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{71} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{72} & = & \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{73} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{74} & = & \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{75} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{76} & = & z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{77} & = & z_{8} \, \mathbf{a}_{1} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{78} & = & z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{79} & = & \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{80} & = & \left(2x_{8}-z_{8}\right) \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{8} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{8}\right)a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{81} & = & -z_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{82} & = & -z_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{83} & = & \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{84} & = & \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{1} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{85} & = & \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{86} & = & \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{87} & = & -z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{88} & = & -z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{89} & = & -z_{8} \, \mathbf{a}_{1} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{90} & = & -z_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{2} + \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{8}\right)a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{91} & = & \left(\frac{1}{2} +2x_{8} + z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{8}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{92} & = & \left(-2x_{8}+z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{93} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{94} & = & z_{9} \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{y}} + z_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{95} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{96} & = & \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{97} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{98} & = & \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & z_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{99} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{100} & = & z_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{x}} + x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{101} & = & z_{9} \, \mathbf{a}_{1} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{102} & = & z_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{2} + z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{x}} + z_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{103} & = & \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{104} & = & \left(2x_{9}-z_{9}\right) \, \mathbf{a}_{1} + z_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{9} - z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{9}\right)a \, \mathbf{\hat{y}} + x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{105} & = & -z_{9} \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{106} & = & -z_{9} \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-z_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{107} & = & \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{108} & = & \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{1} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{109} & = & \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{110} & = & \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{111} & = & -z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{112} & = & -z_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{x}}-z_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{113} & = & -z_{9} \, \mathbf{a}_{1} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{114} & = & -z_{9} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{2} + \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{9}\right)a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{115} & = & \left(\frac{1}{2} +2x_{9} + z_{9}\right) \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{9}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{116} & = & \left(-2x_{9}+z_{9}\right) \, \mathbf{a}_{1}-z_{9} \, \mathbf{a}_{2}-z_{9} \, \mathbf{a}_{3} & = & -z_{9}a \, \mathbf{\hat{x}}-x_{9}a \, \mathbf{\hat{y}}-x_{9}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O III} \\ \mathbf{B}_{117} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{118} & = & z_{10} \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{y}} + z_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{119} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{120} & = & \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{121} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{122} & = & \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & z_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{123} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{124} & = & z_{10} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{x}} + x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{125} & = & z_{10} \, \mathbf{a}_{1} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{126} & = & z_{10} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{2} + z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{x}} + z_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{127} & = & \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{128} & = & \left(2x_{10}-z_{10}\right) \, \mathbf{a}_{1} + z_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{10} - z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{10}\right)a \, \mathbf{\hat{y}} + x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{129} & = & -z_{10} \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{130} & = & -z_{10} \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-z_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{131} & = & \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{132} & = & \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{1} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{133} & = & \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{134} & = & \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{135} & = & -z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{136} & = & -z_{10} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{x}}-z_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{137} & = & -z_{10} \, \mathbf{a}_{1} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{138} & = & -z_{10} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{2} + \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{10}\right)a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{139} & = & \left(\frac{1}{2} +2x_{10} + z_{10}\right) \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{10}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{140} & = & \left(-2x_{10}+z_{10}\right) \, \mathbf{a}_{1}-z_{10} \, \mathbf{a}_{2}-z_{10} \, \mathbf{a}_{3} & = & -z_{10}a \, \mathbf{\hat{x}}-x_{10}a \, \mathbf{\hat{y}}-x_{10}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O IV} \\ \mathbf{B}_{141} & = & z_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + z_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{142} & = & z_{11} \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{y}} + z_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{143} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{144} & = & \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{145} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & z_{11}a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{146} & = & \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & z_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{147} & = & z_{11} \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{148} & = & z_{11} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{x}} + x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{149} & = & z_{11} \, \mathbf{a}_{1} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + z_{11}a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{150} & = & z_{11} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{2} + z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{x}} + z_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{151} & = & \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{152} & = & \left(2x_{11}-z_{11}\right) \, \mathbf{a}_{1} + z_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{11} - z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{11}\right)a \, \mathbf{\hat{y}} + x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{153} & = & -z_{11} \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{y}}-z_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{154} & = & -z_{11} \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}}-z_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{155} & = & \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{156} & = & \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{1} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{157} & = & \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{158} & = & \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{159} & = & -z_{11} \, \mathbf{a}_{1} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-z_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{160} & = & -z_{11} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{x}}-z_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{161} & = & -z_{11} \, \mathbf{a}_{1} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{162} & = & -z_{11} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{2} + \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{11}\right)a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{163} & = & \left(\frac{1}{2} +2x_{11} + z_{11}\right) \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -z_{11}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{11}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \mathbf{B}_{164} & = & \left(-2x_{11}+z_{11}\right) \, \mathbf{a}_{1}-z_{11} \, \mathbf{a}_{2}-z_{11} \, \mathbf{a}_{3} & = & -z_{11}a \, \mathbf{\hat{x}}-x_{11}a \, \mathbf{\hat{y}}-x_{11}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{W} \\ \end{array} \]

References

  • A. J. Bradley and J. W. Illingworth, The Crystal Structure of H3PW12O40·29H2O, Proc. Roy. Soc. Lond. A 157, 113–131 (1936), doi:10.1098/rspa.1936.0183.
  • C. J. Clark and D. Hall, Dodecamolybdophosphoric acid circa 30–hydrate, Acta Crystallogr. Sect. B Struct. Sci. 32, 1545–1547 (1976), doi:10.1107/S0567740876005748.

Found in

  • C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).

Geometry files


Prototype Generator

aflow --proto=A29B40CD12_cF656_227_ae2fg_e3g_b_g --params=

Species:

Running:

Output: