# Fm3m, Fm3c

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay

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 octant of the cube or stereogram might be present, only that octant is portrayed.

 225      Fm3mOrigins: (0,0,0); (1/2,0,1/2); (0,1/2,1/2), (1/2,1/2,0) Hexoctahedral point groups in an F lattice (+x, +y, +z); (+z, +x, +y); (+y, +z, +x); (+x, +z, +y); (+y, +x, +z); (+z, +y, +x)(+x, -y, -z); (+z, -x, -y); (+y, -z, -x); (+x, -z, -y); (+y, -x, -z); (+z, -y, -x)(-x, +y, -z); (-z, +x, -y); (-y, +z, -x); (-x, +z, -y); (-y, +x, -z); (-z, +y, -x)(-x, -y, +z); (-z, -x, +y); (-y, -z, +x); (-x, -z, +y); (-y, -x, +z); (-z, -y, +x)(-x, -y, -z); (-z, -x, -y); (-y, -z, -x); (-x, -z, -y); (-y, -x, -z); (-z, -y, -x)(-x, +y, +z); (-z, +x, +y); (-y, +z, +x); (-x, +z, +y); (-y, +x, +z); (-z, +y, +x)(+x, -y, +z); (+z, -x, +y); (+y, -z, +x); (+x, -z, +y); (+y, -x, +z); (+z, -y, +x)(+x, +y, -z); (+z, +x, -y); (+y, +z, -x); (+x, +z, -y); (+y, +x, -z); (+z, +y, -x) 226      Fm3cOrigins: (0,0,0); (1/2,0,1/2); (0,1/2,1/2), (1/2,1/2,0) Alternating left- and right-handed tetrahedral point groups, in two interpenetrating f lattices. Only the front layer of stereograms is visible in the orthogonal view.