Great dipentary trishecatonicosachoron

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Great dipentary trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGidipthi
Coxeter diagramo5o3x5/3x5/2*b ()
Elements
Cells120 icosahedra, 120 small stellated dodecahedra, 120 great dodecicosidodecahedra
Faces2400 triangles, 1440 pentagrams, 720 decagrams
Edges3600+3600
Vertices1440
Vertex figurePentagonal frustum, edge lengths 1 (large base), (5–1)/2 (small base), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–10/3–gaddid: 144°
 Gaddid–5/2–sissid: 144°
 Gaddid–3–ike: 120°
Number of external pieces6600
Related polytopes
ArmySemi-uniform Tex, edge lengths (icosahedra), (surrounded by truncated tetrahedra)
RegimentGidipthi
ConjugateSmall dipentary trishecatonicosachoron
Abstract & topological properties
Flag count86400
Euler characteristic–1560
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great dipentary trishecatonicosachoron, or gidipthi, is a nonconvex uniform polychoron that consists of 120 icosahedra, 120 small stellated dodecahedra, and 120 great dodecicosidodecahedra. 1 icosahedron, 1 small stellated dodecahedron, and 5 great dodecicosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

The vertices of a great dipentary trishecatonicosachoron of edge length 1 are given by all permutations of:

plus all even permutations of:

Related polychora[edit | edit source]

The great dipentary trishecatonicosachoron is the colonel of a regiment that includes 81 uniform members, as well as 78 fissary uniforms, 18 normal and 59 fissary scaliforms, and 1 scaliform compound.

External links[edit | edit source]