Ridge-facetings of the small rhombicosidodecahedron ship

Possible facets here are the 20 triangles, 30 squares, and 12 pentagons of the comodore itself together with the 12 internal decagons. The general naming code here is accordingly srid-#{3}-#{4}-#{5}-#{10}. This gives rise for exactly 30 edge-facetings with n-gonal axial rotation symmetries, provided n > 2. In fact, 3 have full icosahedral symmetry, 10 have 5-fold pyramidal symmetry, 3 have 5-fold antiprismatic symmetry, 11 have 3-fold pyramidal symmetry, and 3 have 3-fold antiprismatic symmetry.

A well-known edge-faceting with just digonal symmetry (i.e. mirror symmetry) is the Johnson solid J81 (mabidrid).

srid-20-30-12-0 = srid	srid-20-0-12-12 = saddid	srid-0-30-0-12 = sird	srid-5-5-1-1 = pecu	srid-5-15-5-5	srid-5-15-5-7
icosahedral			5-fold pyramidal ...
srid-5-25-1-11	srid-10-10-6-6-a	srid-10-10-6-6-b	srid-10-20-6-6	srid-15-5-11-11	srid-15-15-7-5
... 5-fold pyramidal ...
srid-15-25-11-1 = dirid	srid-10-10-10-10	srid-10-20-2-10	srid-10-20-10-2 = pabidrid	srid-5-15-9-3 = tedrid	srid-5-15-9-9
... 5-fold pyr.	5-fold antiprismatic			3-fold pyramidal ...
srid-7-9-3-3	srid-7-21-3-9	srid-10-12-6-6-a	srid-10-12-6-6-b	srid-10-18-6-6-a	srid-10-18-6-6-b
... 3-fold pyramidal ...
srid-13-9-9-9	srid-13-21-9-3	srid-15-15-3-9	srid-6-12-6-6	srid-6-18-6-6	srid-14-12-6-6
... 3-fold pyramidal			3-fold antiprismatic