Great ditrigonal hecatonicosiprismatodishecatonicosachoron

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Great ditrigonal hecatonicosiprismatodishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGid thipady
Coxeter diagramx5x3o5x5/3*b ()
Elements
Cells720 pentagonal prisms, 120 truncated dodecahedra, 120 great ditrigonal dodecicosidodecahedra, 120 quasitruncated dodecadodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagons, 1440 decagons, 1440 decagrams
Edges3600+7200+7200
Vertices7200
Vertex figureIsosceles trapezoidal pyramid, base edge lengths 1, (5–5)/2, (1+5)/2, (5–5)/2; lateral edge lengths 2, 2, (5+5)/2, (5+5)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGidditdid–5–pip: 162°
 Quitdid–4–pip:
 Gidditdid–10/3–quitdid: 144°
 Tid–10–quitdid: 144°
 Gidditdid–3–tid: 120°
Related polytopes
ArmySemi-uniform Prix, edge lengths (truncated dodecahedra), (bases of triangular prisms)
RegimentGid thipady
ConjugateSmall ditrigonal hecatonicosiprismatodishecatonicosachoron
Abstract & topological properties
Flag count230400
Euler characteristic–1560
OrientableYes
Properties
Symmetry[Hecatonicosachoric symmetry
ConvexNo
NatureTame

The great ditrigonal hecatonicosiprismatodishecatonicosachoron, or gid thipady, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated dodecahedra, 120 great ditrigonal dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 pentagonal prism, 1 truncated dodecahedron, 1 great ditrigonal dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

The vertices of a great ditrigonal hecatonicosiprismatodishecatonicosachoron of edge length 1 are given by all permutations of:

Plus all even permutations of:

Related polychora[edit | edit source]

The great ditrigonal hecatonicosiprismatodishecatonicosachoron is the colonel of a 3-member regiment that also includes the great hecatonicosiprismatodishecatonicosachoron and great hecatonicosihecatonicosihecatonicosachoron.

External links[edit | edit source]