Truncated 5-simplex

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Truncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymTix
Coxeter diagramx3x3o3o3o ()
Elements
Tera6 pentachora, 6 truncated pentachora
Cells30 tetrahedra, 15 truncated tetrahedra
Faces60 triangles, 20 hexagons
Edges15+60
Vertices30
Vertex figureTetrahedral pyramid, edge lengths 1 (base) and 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTip–tet–pen:
 Tip–tut–tip:
Central density1
Number of external pieces12
Level of complexity5
Related polytopes
ArmyTix
RegimentTix
DualPentakis hexateron
ConjugateNone
Abstract & topological properties
Flag count3600
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The truncated 5-simplex, also called the truncated hexateron or tix, is a convex uniform 5-polytope. It consists of 6 regular pentachora and 6 truncated pentachora. One pentachoron and 4 truncated pentachora join at each vertex. As the name suggests, it is the truncation of the 5-simplex.

Vertex coordinates[edit | edit source]

The vertices of a truncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

  • .

Representations[edit | edit source]

A truncated 5-simplex has the following Coxeter diagrams:

  • x3x3o3o3o () (full symmetry)
  • xux3oox3ooo3ooo&#xt (A4 axial, pentachoron-first)
  • xuxo oxux3ooox3oooo&#xt (A3×A1 axial, edge-first)
  • xuxo3xooo ooox3oxux&#xt (A2×A2 axial, hexagon-first)

Gallery[edit | edit source]

External links[edit | edit source]