# Grand hecatonicosachoron

Grand hecatonicosachoron Rank4
TypeRegular
SpaceSpherical
Notation
Bowers style acronymGahi
Coxeter diagramo5/2o3o5x (         )
Schläfli symbol{5,3,5/2}
Elements
Cells120 dodecahedra
Faces720 pentagons
Edges720
Vertices120
Vertex figureGreat icosahedron, edge length (1+5)/2
Edge figuredoe 5 doe 5 doe 5 doe 5 doe 5
Measures (edge length 1)
Circumradius$\frac{1+\sqrt5}{2} \approx 1.61803$ Edge radius$\frac{\sqrt{5+2\sqrt5}}{2} \approx 1.53884$ Face radius$\sqrt{\frac{5+2\sqrt5}{5}} \approx 1.37638$ Inradius$\frac{1+\sqrt5}{4} \approx 0.80902$ Hypervolume$15\frac{25+11\sqrt5}{4} \approx 185.98780$ Dichoral angle72°
Central density20
Number of external pieces21600
Level of complexity44
Related polytopes
ArmyEx
RegimentEx
CompanyGohi
DualGreat stellated hecatonicosachoron
ConjugateGreat stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count14400
Euler characteristic0
Schläfli type{5,3,5}
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The grand hecatonicosachoron, or gahi, also commonly called the grand 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 dodecahedra as cells, joining 5 to an edge and 20 to a vertex in the form of a great icosahedron.

It is a faceting of the hexacosichoron, sharing its vertices and edges, and sharing the faces of the great hecatonicosachoron.

## Vertex coordinates

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

## Related polychora

Uniform polychoron compounds composed of grand hecatonicosachora include: