# Great grand hecatonicosachoron

Jump to navigation Jump to search
Great grand hecatonicosachoron
Rank4
TypeRegular
Notation
Bowers style acronymGaghi
Coxeter diagramx5o5/2o3o ()
Schläfli symbol${\displaystyle \{5,5,3\mid 3\}}$
${\displaystyle \{5,5/2,3\}}$
Elements
Cells120 great dodecahedra
Faces720 pentagons
Edges1200
Vertices120
Vertex figureGreat stellated dodecahedron, edge length (1+5)/2
Edge figuregad 5 gad 5 gad 5
Deep holesTriangles
Measures (edge length 1)
Circumradius1
Edge radius${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Face radius${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{10}}}\approx 0.52573}$
Inradius${\displaystyle {\frac {{\sqrt {5}}-1}{4}}\approx 0.30902}$
Hypervolume${\displaystyle 15{\frac {5+{\sqrt {5}}}{4}}\approx 27.13525}$
Dichoral angle72°
Central density76
Number of external pieces10800
Level of complexity33
Related polytopes
ArmyEx, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSishi
DualGreat faceted hexacosichoron
ConjugateSmall stellated hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count14400
Euler characteristic–480
Schläfli type{5,5,3}
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits1
ConvexNo
NatureTame

The great grand hecatonicosachoron, or gaghi, also commonly called the great grand 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great dodecahedra as cells, joining 3 to an edge and 12 to a vertex in the form of a great stellated dodecahedron.

It is a faceting of the small stellated hecatonicosachoron, sharing its vertices and edges. It is the only other regular polychoron to do so.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.

## Related polychora

Uniform polychoron compounds composed of great grand hecatonicosachora include: