Grand stellated hecatonicosachoron

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Grand stellated hecatonicosachoron
Rank4
TypeRegular
Notation
Bowers style acronymGashi
Coxeter diagramx5/2o5o5/2o ()
Schläfli symbol{5/2,5,5/2}
Elements
Cells120 small stellated dodecahedra
Faces720 pentagrams
Edges720
Vertices120
Vertex figureGreat dodecahedron, edge length (5–1)/2
Edge figuresissid 5/2 sissid 5/2 sissid 5/2 sissid 5/2 sissid 5/2
Measures (edge length 1)
Circumradius
Edge radius
Face radius
Inradius
Hypervolume
Dichoral angle72°
Central density66
Number of external pieces7200
Level of complexity16
Related polytopes
ArmyEx, edge length
RegimentGishi
CompanyGishi
DualGrand stellated hecatonicosachoron
ConjugateGreat hecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count14400
Euler characteristic0
Schläfli type{5,5,5}
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The grand stellated hecatonicosachoron, or gashi, also commonly called the grand stellated 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 small stellated dodecahedra as cells, joining 5 to an edge and 12 to a vertex in the form of a great dodecahedron.

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

It is one of two regular star polychora to be self-dual, the other one being the great hecatonicosachoron, which is the conjugate of this polychoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

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

Related polychora[edit | edit source]

Uniform polychoron compounds composed of grand stellated hecatonicosachora include:

External links[edit | edit source]