Small ditetrahedronary hexacosihecatonicosachoron

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Small ditetrahedronary hexacosihecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSidtaxhi
Coxeter diagramo3o3x5/2o3*b ()
Elements
Cells600 tetrahedra, 120 small ditrigonary icosidodecahedra
Faces2400 triangles, 720 pentagrams
Edges3600
Vertices600
Vertex figureSemi-uniform Truncated tetrahedron, edge lengths 1 (triangle edges) and (5–1)/2 (other edges)
Edge figure(tet 3 sidtid 5/2 sidtid 3)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesSidtid–3–tet:
 Sidtid–5/2–sidtid: 144°
Central density2
Number of external pieces2520
Level of complexity9
Related polytopes
ArmyHi, edge length
RegimentSidtaxhi
ConjugateGrand ditetrahedronary hexacosihecatonicosachoron
Abstract & topological properties
Flag count43200
Euler characteristic—600
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small ditetrahedronary hexacosihecatonicosachoron, or sidtaxhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 tetrahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The small ditetrahedronary hexacosihecatonicosachoron contains the vertices of a small rhombicosidodecahedral prism and decagonal duoprism.

It can be formed as a holosnub hecatonicosachoron.

Vertex coordinates[edit | edit source]

The vertices of a small ditetrahedronary hexacosihecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

Related polychora[edit | edit source]

The small ditetrahedronary hexacosihecatonicosachoron is the colonel of a regiment with 37 members, plus 5 fissaries and three compounds (two are subsymmetric), as well as 11 scaliform members plus 54 scaliform fissaries and 2 scaliform compounds.

External links[edit | edit source]