Great hexacosihecatonicosachoron

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Great hexacosihecatonicosachoron
Gixhi-slices.gif
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGixhi
Coxeter diagramo5/2x3x3o (CDel node.pngCDel 5.pngCDel rat.pngCDel 2x.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png)
Elements
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5–1)/2 (base 2) and 3 (sides)
Cells600 truncated tetrahedra, 120 truncated great icosahedra
Faces1200 triangles, 720 pentagrams, 2400 hexagons
Edges3600+3600
Vertices3600
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTiggy–6–tut:
 Tiggy–5/2–tiggy: 72°
 Tut–3–tut:
Central density191
Euler characteristic0
Number of pieces122640
Level of complexity494
Related polytopes
ArmySemi-uniform Srix
RegimentGixhi
ConjugateHexacosihecatonicosachoron
Convex coreHexacosichoron
Topological properties
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great hexacosihecatonicosachoron, or gixhi, is a nonconvex uniform polychoron that consists of 600 truncated tetrahedra and 120 truncated great icosahedra. 2 of each join at each vertex.

It is the medial stage of the truncation series between a great grand stellated hecatonicosachoron and its dual grand hexacosichoron, which makes it the bitruncation of either of these polychora.

Gallery[edit | edit source]

Gixhi sections Bowers.png Card with cell counts, vertex figure, and cross-sections. Gixhi-reg.png

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a great hexacosihecatonicosachoron of edge length 1 are given by all permutations of:

together with all even permutations of:

External links[edit | edit source]