# Small ditetrahedronary dishecatonicosachoron

Small ditetrahedronary dishecatonicosachoron
Rank4
TypeUniform
Notation
Coxeter diagramo3o3o5/3x5*b ()
Elements
Faces1440 pentagons, 720 pentagrams
Edges3600
Vertices600
Vertex figureHypertruncated tetrahedron, edge lengths (1+5)/2 (triangle edges) and (5–1)/2 (other edges)
Edge figure(doe 5 ditdid 5/2 ditdid 5)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 75{\frac {11+5{\sqrt {5}}}{4}}\approx 415.88137}$
Dichoral anglesDitdid–5/2–ditdid: 144°
Ditdid–5–doe: 36°
Central density5
Number of external pieces11160
Level of complexity31
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
ConjugateGrand ditetrahedronary dishecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small ditetrahedronary dishecatonicosachoron, or siddatady, is a nonconvex uniform polychoron that consists of 120 regular dodecahedra and 120 ditrigonary dodecadodecahedra. 4 ditrigonary dodecadodecahedra and 4 dodecahedra join at each vertex.

## Vertex coordinates

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