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Ridge-facetings of the great ditrigonal dodekicosidodecahedron ship

Possible facets here are the 20 triangles, 12 decagrams, and 12 pentagons of the comodore itself together with the 20 internal hexagons. The general naming code here is accordingly gidditdid-#{3}-#{10/3}-#{5}-#{6}. 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.

 
gidditdid-20-12-12-0
= gidditdid
gidditdid-20-0-12-20
= giid
gidditdid-0-12-0-20
= giddy
icosahedral
gidditdid-10-2-6-10 gidditdid-10-6-2-10 gidditdid-10-6-6-10-a gidditdid-10-6-6-10-b gidditdid-10-6-10-10 gidditdid-10-10-6-10
5-fold pyramidal
gidditdid-6-6-6-10 gidditdid-10-6-6-6 gidditdid-10-6-6-10-c gidditdid-10-6-6-10-d gidditdid-10-6-6-14 gidditdid-14-6-6-10
3-fold pyramidal

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