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Possible facets here are the 8 triangles of the comodore itself and the 3 diametral squares.
The general naming code here is accordingly `oct-#{3}-#{4}`.
This gives rise for exactly 4 edge-facetings, without any further restriction.
Only 3 of those have `n`-gonal axial rotation symmetries with `n > 2`.
In fact, just 1 has full octahedral symmetry, 1 has tetrahedral symmetry, and 1 has 4-fold pyramidal symmetry.
The fourth possible edge-faceting has 2-fold briquet symmetry only.

oct-8-0 = oct |
oct-4-3 = thah |
oct-4-1 = squippy | oct-4-2 |

octahedral | tetrahedral | 4-fold pyramidal | 2-fold briquet |

Possible facets here are the 8 triangles and 6 squares of the comodore itself together with the 4 diametral hexagons.
The general naming code here is accordingly `co-#{3}-#{4}-#{6}`.
This gives rise for exactly 7 edge-facetings, without any further restriction.
Only 5 of those have `n`-gonal axial rotation symmetries with `n > 2`.
In fact, 3 have full octahedral symmetry, and 2 have 3-fold pyramidal symmetry.
The other possible edge-facetings have 2-fold briquet symmetry only.

co-8-6-0 = co |
co-8-0-4 = oho |
co-0-6-4 = cho |
co-4-3-1 = tricu | co-4-3-3 | co-4-4-2 | co-4-2-2 |

octahedral | 3-fold pyramidal | 2-fold briquet |

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