Acronym
| ... |

Name
| gid+geihid+gidhid (?) |

Circumradius
| (sqrt(5)-1)/2 = 0.618034 |

Vertex figure | 4[10/4,6/2,10/3] |

General of army | id |

Colonel of regiment | gid |

Looks like a compound of a great icosidodecahedron (gid) plus a great icosihemidodecahedron (geihid) plus a great dodecahemidodecahedron (gidhid), and indeed vertices coincide by 4, edges coincide by three, {10/3} coincide by pairs.

Incidence matrix according to Dynkin symbol

x5/4x3/2x5/3*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 . x5/3*a | 10 | 5 0 5 | * 12 * . x3/2x | 6 | 0 3 3 | * * 20

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