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Ridge-facetings of the octahedron ship

Possible facets here are the 8 triangles of the comodore itself and the 3 diametral squares. The general naming code here is accordingly oct-#{3}-#{4}. This gives rise for exactly 4 edge-facetings, without any further restriction. Only 3 of those have n-gonal axial rotation symmetries with n > 2. In fact, just 1 has full octahedral symmetry, 1 has tetrahedral symmetry, and 1 has 4-fold pyramidal symmetry. The fourth possible edge-faceting has 2-fold briquet symmetry only.

 
oct-8-0
= oct
oct-4-3
= thah
oct-4-1
= squippy
oct-4-2
octahedral tetrahedral 4-fold pyramidal 2-fold briquet


Ridge-facetings of the cuboctahedron ship

Possible facets here are the 8 triangles and 6 squares of the comodore itself together with the 4 diametral hexagons. The general naming code here is accordingly co-#{3}-#{4}-#{6}. This gives rise for exactly 7 edge-facetings, without any further restriction. Only 5 of those have n-gonal axial rotation symmetries with n > 2. In fact, 3 have full octahedral symmetry, and 2 have 3-fold pyramidal symmetry. The other possible edge-facetings have 2-fold briquet symmetry only.

   
co-8-6-0
= co
co-8-0-4
= oho
co-0-6-4
= cho
co-4-3-1
= tricu
co-4-3-3 co-4-4-2 co-4-2-2
octahedral 3-fold pyramidal 2-fold briquet

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