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Ridge-facetings of the small rhombicuboctahedron ship

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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