# Small ditetrahedronary dishecatonicosihexacosichoron

Small ditetrahedronary dishecatonicosihexacosichoron
Rank4
TypeUniform
Notation
Bowers style acronymSiddatdahix
Elements
Cells600 tetrahedra, 120 ditrigonary dodecadodecahedra, 120 icosidodecahedra
Faces2400 triangles, 1440 pentagons, 720 pentagrams
Edges3600
Vertices600
Edge figure(tet 3 id 5 ditdid 5/2 ditdid 5 id 3)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {2}}+{\sqrt {10}}}{2}}\approx 2.28825}$
Hypervolume${\displaystyle 5{\frac {280+129{\sqrt {5}}}{4}}\approx 710.56596}$
Dichoral anglesDitdid–5/2–ditdid: 144°
Ditdid–5–id: 144°
Id–3–tet: ${\displaystyle \arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.37737^{\circ }}$
Central density9
Number of external pieces68760
Level of complexity171
Related polytopes
ArmyHi, edge length ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$
RegimentSidtaxhi
Conjugategrand inverted ditetrahedronary dishecatonicosihexacosichoron
Abstract & topological properties
Flag count72000
Euler characteristic720
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureWild

The small ditetrahedronary dishecatonicosihexacosichoron, or siddatdahix, is a nonconvex uniform polychoron that consists of 120 ditrigonary dodecadodecahedra, 600 tetrahedra, and 120 icosidodecahedra. Four ditrigonary dodecadodecahedra, four tetrahedra, and six icosidodecahedra join at each vertex.

## Vertex coordinates

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