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Runcitruncated hexateron
Orthogonal projection in A5 Coxeter plane
Type	Uniform 5-polytope
4-faces
Cells
Faces
Edges
Vertices
Schläfli symbol	t0,1,3{3,3,3,3}
Coxeter-Dynkin diagram
Vertex figure
Coxeter group	A5
Properties	convex, isogonal

In five dimensional geometry, runcitruncated hexateron (or runcitruncated 5-simplex) is a uniform 5-polytope.

Coordinates

The coordinates can be made in 6-space, as 180 permutations of:

(0,0,1,1,2,3)

This construction exists as one of 64 orthant facets of the runcitruncated hexacross.

Related uniform 5-polytopes

The runcitruncated 5-simplex is one of 19 uniform polytera based on the Coxeter group, all shown here in A₅ Coxeter plane orthographic projections. (Vertices are colored by projection overlap order, red, orange, yellow, green, cyan, blue, purple having progressively more vertices)

A5 polytopes
t0	t1	t2	t0,1	t0,2	t1,2	t0,3
t1,3	t0,4	t0,1,2	t0,1,3	t0,2,3	t1,2,3	t0,1,4
t0,2,4	t0,1,2,3	t0,1,2,4	t0,1,3,4	t0,1,2,3,4

See also

• Other 5-polytopes (regular):
  • Hexateron - {3,3,3,3}
  • Penteract - {4,3,3,3}
  • Pentacross - {3,3,3,4}

References

• Norman Johnson Uniform Polytopes, Manuscript (1991)
• Richard Klitzing 5D quasiregulars, (multi)prisms, non-prismatic Wythoffian polyterons x3x3o3x3o - pattix

External links

• Glossary for hyperspace, George Olshevsky.
• Polytopes of Various Dimensions
• Multi-dimensional Glossary

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