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 = bobipyr
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 = gripper	co-4-4-2 = bocuco	co-4-2-2 = ebot
octahedral			3-fold pyramidal		2-fold briquet