Great grand stellated hecatonicosachoron

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Great grand stellated hecatonicosachoron
Rank4
TypeRegular
Notation
Bowers style acronymGogishi
Coxeter diagramx5/2o3o3o ()
Schläfli symbol{5/2,3,3}
Elements
Cells120 great stellated dodecahedra
Faces720 pentagrams
Edges1200
Vertices600
Vertex figureTetrahedron, edge length (5–1)/2
Edge figuregissid 5/2 gissid 5/2 gissid 5/2
Measures (edge length 1)
Circumradius
Edge radius
Face radius
Inradius
Hypervolume
Dichoral angle72°
Central density191
Number of external pieces9600
Level of complexity30
Related polytopes
ArmyHi, edge length
RegimentGogishi
DualGrand hexacosichoron
ConjugateHecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count14400
Euler characteristic0
Schläfli type{5,3,3}
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great grand stellated hecatonicosachoron, or gogishi, also commonly called the great grand stellated 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great stellated dodecahedra as cells, joining 3 to an edge and 4 to a vertex.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a great grand stellated hecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

  • ,
  • ,
  • ,
  • ,

together with all the even permutations of:

  • ,
  • ,
  • .

Related polychora[edit | edit source]

Uniform polychoron compounds composed of great grand stellated hecatonicosachora include:

External links[edit | edit source]