Small prismatohecatonicosintercepted dishecatonicosachoron

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Small prismatohecatonicosintercepted dishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSophinady
Elements
Cells720 pentagonal prisms, 120 icosidodecahedra, 120 great dodecicosidodecahedra, 120 quasitruncated dodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagons, 720 pentagrams, 720 decagons, 1440 decagrams
Edges3600+7200
Vertices3600
Vertex figureInverted wedge, edge lengths 1 (2), Template:Radi (4), (1+5)/2 (2), (5–1)/2 (1), (5+5)/2 (2), and (5–5)/2 (4)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–5/2–gaddid: 144°
 Gaddid–10/3–quitdid: 72°
 Gaddid–3–id: 60°
 Quitdid–4–pip:
 Id–5–pi: 54°
 Quitdid–10–quitdid: 36°
Related polytopes
ArmySemi-uniform srix
RegimentWavathi
ConjugateHecatonicosintercepted hecatonicosiprismatohecatonicosachoron
Abstract & topological properties
Euler characteristic2040
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small prismatohecatonicosintercepted dishecatonicosachoron, or sophinady, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra, 120 great dodecicosidodecahedra, 720 pentagonal prisms, and 120 quasitruncated dodecadodecahedra. One icosidodecahedron, two great dodecicosidodecahedra, two pentagonal prisms, and four quasitruncated dodecadodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

The vertices are the same as those of the regiment colonel, the sphenoverted trishecatonicosachoron.

External links[edit | edit source]