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Possible facets here are the 20 triangles and 12 pentagons of the comodore itself together with the 6 internal decagons.
The general naming code here is accordingly `id-#{3}-#{5}-#{10}`.
This gives rise for exactly 7 edge-facetings with `n`-gonal axial rotation symmetries, provided `n > 2`.
In fact, 3 have full icosahedral symmetry, 2 have 5-fold pyramidal symmetry, and 2 have 3-fold pyramidal symmetry.

id-20-12-0 = id |
id-20-0-6 = seihid |
id-0-12-6 = sidhid |
id-10-6-1 = pero | id-10-6-5 | id-10-6-3-a | id-10-6-3-b |

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

Possible facets here are the 12 pentagrams and 20 triangles of the comodore itself together with the 6 internal decagrams.
The general naming code here is accordingly `gid-#{5/2}-#{3}-#{10/3}`.
This gives rise for exactly 7 edge-facetings with `n`-gonal axial rotation symmetries, provided `n > 2`.
In fact, 3 have full icosahedral symmetry, 2 have 5-fold pyramidal symmetry, and 2 have 3-fold pyramidal symmetry.

gid-12-20-0 = gid |
gid-12-0-6 = gidhid |
gid-0-20-6 = geihid | gid-6-10-1 | gid-6-10-5 | gid-6-10-3-a | gid-6-10-3-b |

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

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