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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
= gad
= teddi
ike-7-3 ike-13-3 ike-6-6-a ike-6-6-b
icosahedral 3-fold pyramidal 3-fold antiprismatic
= peppy
ike-5-5 ike-5-7 ike-10-6 ike-15-1
= gyepip
= pap
5-fold pyramidal 5-fold antipr.

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