Grand hecatonicosachoron

Grand hecatonicosachoron
Rank4
TypeRegular
Notation
Bowers style acronymGahi
Coxeter diagramo5/2o3o5x ()
Schläfli symbol{5,3,5/2}
${\displaystyle \{5,3,5\mid 3\}}$[1]
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
Deep holes1200 triangles[1]
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${\displaystyle {\frac {1+{\sqrt {5}}}{4}}\approx 0.80902}$
Hypervolume${\displaystyle 15{\frac {25+11{\sqrt {5}}}{4}}\approx 185.98780}$
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: