# Great hecatonicosachoron

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
Measures (edge length 1)
Circumradius${\displaystyle {\frac {1+{\sqrt {5}}}{2}}\approx 1.61803}$
Edge radius${\displaystyle {\frac {\sqrt {5+2{\sqrt {5}}}}{2}}\approx 1.53884}$
Face radius${\displaystyle {\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\approx 1.37638}$
Inradius${\displaystyle {\frac {3+{\sqrt {5}}}{4}}\approx 1.30902}$
Hypervolume${\displaystyle 15{\frac {15+7{\sqrt {5}}}{4}}\approx 114.94678}$
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.

## Vertex coordinates

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

## Related polychora

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: