Antifrustary hexacositrishecatonicosachoron

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Antifrustary hexacositrishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymAffixthi
Coxeter diagramx3o5x5/2o3*a5/3*c
Elements
Cells600 octahedra, 120 dodecadodecahedra, 120 great dodecicosidodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces2400+2400 triangles, 1440 pentagons, 1440 pentagrams, 1440 decagrams
Edges7200+7200
Vertices3600
Vertex figureRectangular frustum, edge lengths 1 (top square), (1+5)/2 and (5–1)/2 (base rectangle), and (5–5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesOct–3–gaddid:
 Did–5/2–gaddid: 144°
 Did–5–gidditdid: 144°
 Gaddid–10/3–gidditdid: 144°
 Oct–3–gidditdid:
Number of external pieces12720
Related polytopes
ArmySemi-uniform Xhi, edge lengths (pentagons), (triangles)
RegimentAffixthi
ConjugateRetrofrustary hexacositrishecatonicosachoron
Abstract & topological properties
Flag count172800
Euler characteristic–2640
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The antifrustary hexacositrishecatonicosachoron, or affixthi, is a nonconvex uniform polychoron that consists of 600 octahedra, 120 dodecadodecahedra, 120 great dodecicosidodecahedra, and 120 great ditrigonal dodecicosidodecahedra. 1 octahedron, 1 dodecadodecahedron, 2 great dodecicosidodecahedra, and 2 great ditrigonal dodecicosidodecahedra join at each vertex.

The antifrustary hexacositrishecatonicosachoron contains the vertices of a great prismatodecachoron.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an antifrustary hexacositrishecatonicosachoron of edge length 1 are given by all permutations of:

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  • ,
  • ,
  • ,
  • ,

together with all even permutations of:

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  • ,
  • ,
  • ,
  • ,
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  • ,
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  • ,
  • ,
  • ,
  • .

Related polychora[edit | edit source]

The antifrustary hexacositrishecatonicosachoron is the colonel of a regiment of 99 members, plus one fissary and one compound.

External links[edit | edit source]