Sphenoverted trishecatonicosachoron

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Sphenoverted trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymWavathi
Coxeter diagramo5x3o5/2x5/3*b ()
Elements
Cells120 icosidodecahedra, 120 quasitruncated small stellated dodecahedra, 120 great dodecicosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 pentagrams, 1440 decagrams
Edges3600+7200
Vertices3600
Vertex figureWedge, edge lengths (1+5)/2 (two edges of base rectangle), 1 (remaining base edges), (5–5)/2 (side edges), and (5–1)/2 (top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–5/2–gaddid: 144°
 Gaddid–10/3–quit sissid: 144°
 Id–5–quit sissid: 72°
 Gaddid–3–id: 60°
Number of external pieces7560
Related polytopes
ArmySemi-uniform Srix, edge lengths (icosidodecahedra), (main triangles)
RegimentWavathi
ConjugateRetrosphenoverted trishecatonicosachoron
Abstract & topological properties
Flag count129600
Euler characteristic–1560
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The sphenoverted trishecatonicosachoron, or wavathi, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 icosidodecahedra, and 120 great dodecicosidodecahedra. 1 icosidodecahedron, 2 quasitruncated small stellated dodecahedra, and 2 great dodecicosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a sphenoverted trishecatonicosachoron of edge length 1 are given by all permutations of:

together with all even permutations of:

Related polychora[edit | edit source]

The sphenoverted trishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasirhombated great stellated hecatonicosachoron, great rhombic hecatonicosihecatonicosachoron, pseudorhombic hecatonicosihecatonicosachoron, grand quasirhombic hecatonicosihecatonicosachoron, small prismatohecatonicosintercepted dishecatonicosachoron, and great hecatonicosintercepted trishecatonicosachoron.

External links[edit | edit source]