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Possible facets here are the 12 pentagrams and 12 pentagons of the comodore itself together with the 20 internal hexagons.
The general naming code here is accordingly `did-#{5/2}-#{5}-#{6}`.
This gives rise for exactly 7 edge-facetings with `n`-gonal axial rotation symmetries, where `n > 2`.
In fact, 3 have full icosahedral symmetry, 2 have 5-fold pyramidal symmetry, and 2 have 3-fold pyramidal symmetry.

did-12-12-0 = did |
did-12-0-10 = sidhei |
did-0-12-10 = gidhei | did-6-6-5-a | did-6-6-5-b | did-6-6-3 | did-6-6-7 |

icosahedral | 5-fold pyramidal | 3-fold pyramidal |

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