Great hecatonicosachoron

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Great hecatonicosachoron
Rank4
TypeRegular
Notation
Bowers style acronymGohi
Coxeter diagramx5o5/2o5o ()
Schläfli symbol{5,5/2,5}
Elements
Cells120 great dodecahedra
Faces720 pentagons
Edges720
Vertices120
Vertex figureSmall stellated dodecahedron, edge length (1+5)/2
Edge figuregad 5 gad 5 gad 5 gad 5 gad 5
Measures (edge length 1)
Circumradius
Edge radius
Face radius
Inradius
Hypervolume
Dichoral angle144°
Central density6
Number of external pieces3600
Level of complexity6
Related polytopes
ArmyEx
RegimentEx
CompanyGohi
DualGreat hecatonicosachoron
ConjugateGrand stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count14400
Euler characteristic0
Schläfli type{5,5,5}
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits1
ConvexNo
NatureTame

The great hecatonicosachoron, or gohi, also commonly called the great 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great dodecahedra as cells, joining 5 to an edge and 12 to a vertex in the form of a small stellated dodecahedron.

It is a faceting of the hexacosichoron, sharing its vertices and edges. The great dodecahedral cells are in the vertex-figure planes of the hexacosichoron.

It is one of two regular star polychora to be self-dual, the other one being the grand stellated hecatonicosachoron, which is the conjugate of this polychoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the hexacosichoron.

Related polychora[edit | edit source]

The great hecatonicosachoron is the captain of a company in the regiment of the hexacosichoron, having the same faces as the grand hecatonicosachoron.

Uniform polychoron compounds composed of great hecatonicosachora include:

External links[edit | edit source]