Great rhombated faceted hexacosichoron

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Great rhombated faceted hexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymGirfix
Coxeter diagramo5/2x5x3x ()
Elements
Cells720 pentagrammic prisms, 120 truncated great dodecahedra, 120 great rhombicosidodecahedra
Faces3600 squares, 1440 pentagrams, 1200 hexagons, 1440 decagons
Edges3600+3600+7200
Vertices7200
Vertex figureSphenoid, edge lengths 2 (1), (5–1)/2 (2), 3 (1), and (5+5)/2 (2)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTigid–5/2–stip: 162°
 Grid–4–stip:
 Grid–10–tigid: 144°
 Grid–6–grid: 120°
Number of external pieces3240
Level of complexity29
Related polytopes
ArmySemi-uniform Grix, edge lengths (pentagons), 1 (main hexagons)
RegimentGirfix
ConjugateGreat quasirhombated great faceted hexacosichoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count172800
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great rhombated faceted hexacosichoron, or girfix, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 truncated great dodecahedra, and 120 great rhombicosidodecahedra. 1 pentagrammic prism, 1 truncated great dodecahedron, and 2 great rhombicosidodecahedra join at each vertex. As the names suggests, it can be obtained by cantitruncating the faceted hexacosichoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great rhombated faceted hexacosichoron of edge length 1 are given by all permutations of:

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plus all even permutations of:

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External links[edit | edit source]