# Small ditetrahedronary hexacosidishecatonicosachoron

Small ditetrahedronary hexacosidishecatonicosachoron
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramo3o3o3x5*a3/2*c ()
Elements
Cells600 tetrahedra, 120 dodecahedra, 120 great ditrigonary icosidodecahedra
Faces2400 triangles, 1440 pentagons
Edges3600
Vertices600
Vertex figureGreat tetradistetrahedron, edge lengths 1 and (1+5)/2
Edge figure(tet 3 gidtid 5 doe 5 gidtid 3)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2+\sqrt{10}}{2} ≈ 2.28825}$
Hypervolume${\displaystyle 5\frac{265+112\sqrt5}{4} ≈ 644.29952}$
Dichoral anglesGidtid–5–doe: 36°
Gidtid–3–tet: ${\displaystyle \arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876^\circ}$
Central density7
Number of external pieces16920
Level of complexity43
Related polytopes
ArmyHi
RegimentSidtaxhi
ConjugateGrand retroditetrahedronary hexacosidishecatonicosachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small ditetrahedronary hexacosidishecatonicosachoron, or sidtaxady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 great ditrigonary icosidodecahedra. 4 dodecahedra, 4 tetrahedra, and 4 great ditrigonary icosidodecahedra join at each vertex.

## Vertex coordinates

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