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Ridge-facetings of the rhombidodecadodecahedron ship

Possible facets here are the 12 pentagrams, 30 squares, and 12 pentagons of the comodore itself together with the 20 internal hexagons. The general naming code here is accordingly raded-#{5/2}-#{4}-#{5}-#{6}. This gives rise for exactly 33 edge-facetings with n-gonal axial rotation symmetries, where n > 2. In fact, 3 have full icosahedral symmetry, 12 have 5-fold pyramidal symmetry, 2 have 5-fold antiprismatic symmetry, 12 have 3-fold pyramidal symmetry, and 4 have 3fold antiprismatic symmetry.

raded-12-30-12-0
= raded
raded-12-0-12-20
= ided
raded-0-30-0-20
= ri
raded-1-10-5-5 raded-1-20-5-15 raded-5-10-1-5 raded-5-20-1-15
icosahedral 5-fold pyramidal ...
raded-6-10-6-10-a raded-6-10-6-10-b raded-6-20-6-10-a raded-6-20-6-10-b raded-7-10-11-15 raded-7-20-11-5 raded-11-10-7-15
... 5-fold pyramidal ...
raded-11-20-7-5 raded-2-10-10-10 raded-10-10-2-10 raded-3-6-3-5 raded-3-12-3-7 raded-3-18-3-13 raded-3-24-3-15
... 5-fold pyr. 5-fold antiprismatic 3-fold pyramidal ...
raded-6-12-6-10-a raded-6-12-6-10-b raded-6-18-6-10-a raded-6-18-6-10-b raded-9-6-9-15 raded-9-12-9-13 raded-9-18-9-7
... 3-fold pyramidal ...
 
raded-9-24-9-5 raded-6-12-6-6 raded-6-12-6-14 raded-6-18-6-6 raded-6-18-6-14
... 3-fold pyr. 3-fold antiprismatic

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