# Small retroinverted ditetrahedronary trishecatonicosachoron

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Small retroinverted ditetrahedronary trishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSridtathi
Elements
Cells120 dodecahedra, 120 small ditrigonary icosidodecahedra, 120 icosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 pentagrams
Edges3600
Vertices600
Vertex figureSemi-uniform inverted truncated tetrahedron, edge lengths 1 (triangle edges) and (5–1)/2 (other edges)
Edge figure(doe 5 id 3 sidtid 5/2 sidtid 3 id 5)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 5{\frac {505+231{\sqrt {5}}}{4}}\approx 1276.91463}$
Dichoral anglesSidtid–5/2–sidtid: 144°
Sidtid–3–id: 120°
Doe–5–id: 72°
Number of external pieces7320
Level of complexity17
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
ConjugateGrand inverted ditetrahedronary trishecatonicosachoron
Abstract & topological properties
Flag count72000
Euler characteristic1200
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small retroinverted ditetrahedronary trishecatonicosachoron, or sridtathi, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra, 120 dodecahedra, and 120 icosidodecahedra. Four small ditrigonary icosidodecahedra, four dodecahedra, and six icosidodecahedra join at each vertex.

## Vertex coordinates

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