Acronym
| ... |

Name
| did+sidhei+gidhei (?) |

Circumradius
| 1 |

Vertex figure | 4[10/4,10/2,6] |

General of army | id |

Colonel of regiment | did |

Looks like a compound of a dodecadodecahedron (did) plus a small dodecahemicosahedron (sidhei) plus a great dodecahemicosahedron (gidhei), and indeed vertices coincide by 4, edges coincide by three, {6} coincide by pairs.

Incidence matrix according to Dynkin symbol

x5/4x5/2x3*a . . . | 120 | 1 1 1 | 1 1 1 -------------+-----+----------+--------- x . . | 2 | 60 * * | 1 1 0 . x . | 2 | * 60 * | 1 0 1 . . x | 2 | * * 60 | 0 1 1 -------------+-----+----------+--------- x5/4x . | 10 | 5 5 0 | 12 * * x . x3*a | 6 | 3 0 3 | * 20 * . x5/2x | 10 | 0 5 5 | * * 12

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