Acronym
| ... |

Name
| id+seihid+sidhid (?) |

Circumradius
| (1+sqrt(5))/2 = 1.618034 |

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

General of army | id |

Colonel of regiment | id |

Looks like a compound of an icosidodecahedron (id), a small icosihemidodecahedron (seihid), and a small dodecahemidodecahedron (sidhid), and indeed vertices coincide by 4, edges coincide by three, {10} coincide by pairs.

Incidence matrix according to Dynkin symbol

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

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