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Ridge-facetings of the small icosicosidodecahedron ship

Possible facets here are the 12 pentagrams, 20 triangles, and 20 hexagons of the comodore itself together with the 12 internal decagons. The general naming code here is accordingly siid-#{5/2}-#{3}-#{6}-#{10}. This gives rise for exactly 15 edge-facetings with n-gonal axial rotation symmetries, where n > 2. In fact, 3 have full icosahedral symmetry, 6 have 5-fold pyramidal symmetry, and 6 have 3-fold pyramidal symmetry.

 
siid-12-20-20-0
= siid
siid-12-20-0-12
= sidditdid
siid-0-0-20-12
= siddy
icosahedral
siid-2-10-10-6 siid-6-10-10-2 siid-6-10-10-6-a siid-6-10-10-6-b siid-6-10-10-10 siid-10-10-10-6
5-fold pyramidal
siid-6-6-10-6 siid-6-10-6-6 siid-6-10-10-6-c siid-6-10-10-6-d siid-6-10-14-6 siid-6-14-10-6
3-fold pyramidal

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