Ridge-facetings of the icosahedron ship

Possible facets here are the 20 triangles of the comodore itself together with the 12 internal pentagons. The general naming code here is accordingly ike-#{3}-#{5}. This gives rise for exactly 13 edge-facetings with n-gonal axial rotation symmetries, where n > 2. In fact, 2 have full icosahedral symmetry, 5 have 5-fold pyramidal symmetry, 1 has 5-fold antiprismatic symmetry, 3 have 3-fold pyramidal symmetry, and 2 have 3-fold antiprismatic symmetry.

A well-known edge-faceting with just digonal symmetry (i.e. mirror symmetry) is the Johnson solid J62 (mibdi).

ike-20-0 = ike	ike-0-12 = gad	ike-5-3 = teddi	ike-7-3 = scuffi	ike-13-3 = ib	ike-6-6-a = toif	ike-6-6-b = tigdaf
icosahedral		3-fold pyramidal			3-fold antiprismatic
ike-5-1 = peppy	ike-5-5 = gadcone	ike-5-7 = digdom	ike-10-6 = igdom	ike-15-1 = gyepip	ike-10-2 = pap	ike-6-2 = ifbah
5-fold pyramidal					5-fold antipr.	some 2-fold