Retroditetrahedronary trishecatonicosachoron

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Retroditetrahedronary trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymRadatathi
Coxeter diagramo3o3o5x5/3*a ()
Elements
Cells120 dodecahedra, 120 great stellated dodecahedra, 120 dodecadodecahedra
Faces1440 pentagons, 1440 pentagrams
Edges3600
Vertices600
Vertex figureQuasirhombitetratetrahedron, edge lengths (5–1)/2 and (1+5)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesDoe–5–did: 144°
 Gissid–5/2–did: 72°
Central density65
Number of external pieces45720
Level of complexity105
Related polytopes
ArmyHi, edge length
RegimentDattady
CompanyDattathi
ConjugateRetroditetrahedronary dishecatonicosachoron
Abstract & topological properties
Flag count57600
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The retroditetrahedronary trishecatonicosachoron, or radatathi, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, and 120 dodecadodecahedra. 4 great stellated dodecahedra, 4 dodecahedra, and 6 dodecadodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the ditetrahedronary dishecatonicosachoron.

External links[edit | edit source]