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Possible facets here are the 8 triangles and 18 squares (6 in cubic and 12 in rhombic position) of the comodore itself together with the 6 internal octagons. The general naming code here is accordingly sirco-#{3}-#{4}-#{8}. This gives rise for exactly 12 edge-facetings with n-gonal axial rotation symmetries, provided n > 2. In fact, 3 have full octahedral symmetry, 3 have 4-fold prismatic symmetry, 4 have 4-fold pyramidal symmetry, and 2 have 3-fold pyramidal symmetry.
sirco-8-18-0 = sirco |
sirco-8-6-6 = socco |
sirco-0-12-6 = sroh |
sirco-0-8-2 = op |
sirco-0-12-4 = topfu |
sirco-8-6-4 = tepcus |
octahedral | 4-fold prismatic | ||||
sirco-4-5-1 = squacu | sirco-4-9-5-a | sirco-4-9-5-b |
sirco-4-13-1 = escu | sirco-4-9-3-a | sirco-4-9-3-b |
4-fold pyramidal | 3-fold pyramidal |
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