# P23, F23, I23

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay);
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For the isometric space groups, we encounter a visualization problem. There is no longer a single principal symmetry direction we can look along. The diagonal 3-fold symmetry axes rotate the motif into planes perpendicular to the plane of the diagram so they are seen edgewise. So for isometric space groups,  three modes of visualization are employed. First is an oblique drawing of the cubic unit cell with the R motif on a smaller cube. Second is an oblique drawing with stereograms replacing the small cube. The stereograms are drawn in standard crystallographic style without any attempt to represent the projections in perspective. Finally there is a view of the unit cell and stereograms viewed perpendicular to a face. For cases like screw axes where only one or two octants of the cube or stereogram might contain motifs, only those octants are portrayed.

 195     P23 Simple space group. 23 clusters in a P lattice (+x,+y,+z); (+z,+x,+y); (+y,+z,+x); (+x,-y,-z); (+z,-x,-y); (+y,-z,-x); (-x,+y,-z); (-z,+x,-y); (-y,+z,-x); (-x,-y,+z); (-z,-x,+y); (-y,-z,+x) 196     F23 Origins: (0,0,0; (0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0) Simple space group. 23 clusters in an F lattice (+x,+y,+z); (+z,+x,+y); (+y,+z,+x); (+x,-y,-z); (+z,-x,-y); (+y,-z,-x); (-x,+y,-z); (-z,+x,-y); (-y,+z,-x); (-x,-y,+z); (-z,-x,+y); (-y,-z,+x) 197     I23 Origins: (0,0,0; 1/2,1/2,1/2) Simple space group. 23 clusters in an I lattice (+x,+y,+z); (+z,+x,+y); (+y,+z,+x); (+x,-y,-z); (+z,-x,-y); (+y,-z,-x); (-x,+y,-z); (-z,+x,-y); (-y,+z,-x); (-x,-y,+z); (-z,-x,+y); (-y,-z,+x)