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Possible facets here are the 12 pentagrams of the comodore itself together with the 20 internal triangles.
The general naming code here is accordingly `sissid-#{5/2}-#{3}`.
This gives rise for exactly 13 edge-facetings with `n`-gonal axial rotation symmetries, where `n > 2`.
In fact, 2 have full icosahedral symmetry, 5 have 5-fold pyramidal symmetry, 1 has 5-fold antiprismatic symmetry,
3 have 3-fold pyramidal symmetry, and 2 have 3-fold antiprismatic symmetry.

sissid-12-0 = sissid |
sissid-0-20 = gike |
sissid-3-5 = targi | sissid-3-7 | sissid-3-13 | sissid-6-6-a | sissid-6-6-b |

icosahedral | 3-fold pyramidal | 3-fold antiprismatic | ||||

sissid-1-5 = stappy | sissid-1-15 | sissid-5-5 | sissid-6-10 | sissid-7-5 |
sissid-2-10 = starp | |

5-fold pyramidal | 5-fold antipr. |

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