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Possible facets here are the 20 triangles, 30 squares, and 12 pentagons of the comodore itself together with the 12 internal decagons.
The general naming code here is accordingly `srid-#{3}-#{4}-#{5}-#{10}`.
This gives rise for exactly 30 edge-facetings with `n`-gonal axial rotation symmetries, provided `n > 2`.
In fact, 3 have full icosahedral symmetry, 10 have 5-fold pyramidal symmetry, 3 have 5-fold antiprismatic symmetry,
11 have 3-fold pyramidal symmetry, and 3 have 3-fold antiprismatic symmetry.

A well-known edge-faceting with just digonal symmetry (i.e. mirror symmetry) is the Johnson solid J81 (mabidrid).

srid-20-30-12-0 = srid |
srid-20-0-12-12 = saddid |
srid-0-30-0-12 = sird |
srid-5-5-1-1 = pecu | srid-5-15-5-5 | srid-5-15-5-7 |

icosahedral | 5-fold pyramidal ... | ||||

srid-5-25-1-11 | srid-10-10-6-6-a | srid-10-10-6-6-b | srid-10-20-6-6 | srid-15-5-11-11 | srid-15-15-7-5 |

... 5-fold pyramidal ... | |||||

srid-15-25-11-1 = dirid | srid-10-10-10-10 | srid-10-20-2-10 |
srid-10-20-10-2 = pabidrid |
srid-5-15-9-3 = tedrid | srid-5-15-9-9 |

... 5-fold pyr. | 5-fold antiprismatic | 3-fold pyramidal ... | |||

srid-7-9-3-3 | srid-7-21-3-9 | srid-10-12-6-6-a | srid-10-12-6-6-b | srid-10-18-6-6-a | srid-10-18-6-6-b |

... 3-fold pyramidal ... | |||||

srid-13-9-9-9 | srid-13-21-9-3 | srid-15-15-3-9 | srid-6-12-6-6 | srid-6-18-6-6 | srid-14-12-6-6 |

... 3-fold pyramidal | 3-fold antiprismatic |

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