Small dishexacosidishecatonicosachoron

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Small dishexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSadixady
Coxeter diagramx3x3o3o5/2*a ()
Elements
Cells600 tetrahedra, 120 great stellated dodecahedra, 600 truncated tetrahedra, 120 truncated great icosahedra
Faces2400 triangles, 1440 pentagrams, 2400 hexagons
Edges3600+3600
Vertices2400
Vertex figureTriangular antipodium, edge lengths 1 (large base), (5–1)/2 (small base), and 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTet–3–tut:
 Tiggy–6–tut:
 Gissid–5/2–tiggy: 144°
Number of external pieces57120
Level of complexity293
Related polytopes
ArmySemi-uniform Sidpixhi, edge lengths (dodecahedra), (tetrahedra)
RegimentSadixady
ConjugateGreat dishexacosidishecatonicosachoron
Abstract & topological properties
Flag count115200
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small dishexacosidishecatonicosachoron, or sadixady, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, 600 truncated tetrahedra, and 120 truncated great icosahedra. 1 tetrahedron, 1 great stellated dodecahedron, 3 truncated tetrahedra, and 3 truncated great icosahedra join at each vertex.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

The vertices of a small dishexacosidishecatonicosachoron of edge length 1 are given by all permutations of:

along with all even permutations of:

Related polychora[edit | edit source]

The small dishexacosidishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the small hexacosifaceted hexacosidishecatonicosachoron, small hecatonicosafaceted hexacosidishecatonicosachoron, small ditrigonal hecatonicosihexacosihecatonicosachoron, hecatonicosihecatonicosihexacosichoron, small spinotrishecatonicosachoron, and small spinohecatonicosidishexacosichoron.

External links[edit | edit source]