# Great hecatonicosachoron

Great hecatonicosachoron
Rank4
TypeRegular
SpaceSpherical
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${\displaystyle \frac{1+\sqrt5}{2} \approx 1.61803}$
Edge radius${\displaystyle \frac{\sqrt{5+2\sqrt5}}{2} \approx 1.53884}$
Face radius${\displaystyle \sqrt{\frac{5+2\sqrt5}{5}} \approx 1.37638}$
Inradius${\displaystyle \frac{3+\sqrt5}{4} \approx 1.30902}$
Hypervolume${\displaystyle 15\frac{15+7\sqrt5}{4} \approx 114.94678}$
Dichoral angle144°
Central density6
Number of pieces3600
Level of complexity6
Related polytopes
ArmyEx
RegimentEx
CompanyGohi
DualGreat hecatonicosachoron
ConjugateGrand stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH4, order 14400
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.