# Small retroditetrahedronary hexacosidishecatonicosachoron

Small retroditetrahedronary hexacosidishecatonicosachoron
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx3o3/2o3o5*a ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 120 icosidodecahedra
Faces2400 triangles, 1440 pentagons
Edges3600
Vertices600
Vertex figureQuasirhombitetratetrahedron, edge lengths 1 and (1+5)/2
Edge figure(tet 3 id 5 doe 5 id 3)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825}$
Hypervolume${\displaystyle 5\frac{405+194\sqrt5}{4} ≈ 1048.49648}$
Dichoral anglesId–3–tet: ${\displaystyle \arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876°}$
Doe–5–id: 72°
Central density14
Number of external pieces161280
Level of complexity316
Related polytopes
ArmyHi
RegimentSidtaxhi
ConjugateGrand ditetrahedronary hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small retroditetrahedronary hexacosidishecatonicosachoron, or sirdtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 icosidodecahedra. 4 dodecahedra, 4 tetrahedra, and 6 icosidodecahedra join at each vertex.

## Vertex coordinates

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