Snub cellibiprismatoteron

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Snub cellibiprismatoteron
Rank5
TypeUniform
Notation
Bowers style acronymScab
Elements
Tera160+480 triangular-square duoprisms, 80 snub cubic prisms
Cells240+640 triangular prisms, 240+480+480 cubes, 80 snub cubes
Faces640+1920 triangles, 480+960+960+1920 squares
Edges960+1920+1920
Vertices960
Measures (edge length 1)
Circumradius≈ 1.51841
Related polytopes
ArmySemi-uniform Stericantellated 5-cube
RegimentScab
ConjugateSelf
Abstract & topological properties
Flag count337920
OrientableNo
Properties
SymmetryB5+, order 1920
ConvexNo
NatureTame

The snub cellibiprismatoteron or scab is a nonconvex uniform 5-polytope. It consists of 160 triangular-square duoprisms forming 80 pairs, 480 more triangular-square duoprisms, and 80 snub cubic prisms, as well as 10 compounds of 6 tesseracts as pseudofacets. 2+6 triangular-square duoprisms and 4 snub cubic prisms meet at each vertex.

The snub cellibiprismatoteron is the first known non-multiprismatic uniform polytope to contain snub cubes as proper elements, in this case as ridges. However, it can still be constructed by blending 20 square-snub cubic duoprisms on their tesseracts, hence the 6-tesseract pseudo-facets.

Vertex coordinates[edit | edit source]

The vertices of a snub cellibiprismatoteron of edge length 1 are given by all permutations and sign changes of

  • (c1, c1, c2, c2, c3),

where

  • ,
  • ,
  • .

External links[edit | edit source]