Dishecatonicosaquasitruncated dishecatonicosachoron

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Dishecatonicosaquasitruncated dishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymDahiquatady
Coxeter diagramo5x3x5x5/3*b ()
Elements
Cells120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, 120 icosidodecatruncated icosidodecahedra
Faces1440 pentagons, 2400 hexagons, 720 decagons, 1440 decagrams
Edges3600+3600+7200
Vertices7200
Vertex figureSphenoid, edge lengths (1+5)/2 (1), 3 (2), (5+5)/2 (1), and (5–5)/2 (2)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesIdtid–10/3–quit sissid: 144°
 Ti–5–quit sissid: 144°
 Idtid–10–idtid: 144°
 Idtid–6–ti: 120°
Number of external pieces13560
Level of complexity65
Related polytopes
ArmySemi-uniform Prahi, edge lengths (small rhombicosidodecahedra), 1 (sides of pentagonal prisms)
RegimentDahiquatady
ConjugateDishecatonicositruncated dishecatonicosachoron
Convex coreHecatonicosachoron
Abstract & topological properties
Flag count172800
Euler characteristic–1560
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The dishecatonicosaquasitruncated dishecatonicosachoron, or dahiquatady, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, and 120 icosidodecatruncated icosidodecahedra. 1 quasitruncated small stellated dodecahedron, 1 truncated icosahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a dishecatonicosiquasitruncated dishecatonicosachoron of edge length 1 are given by all permutations of:

Plus all even permutations of:

External links[edit | edit source]