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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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