Cantellated 5-orthoplexes

Cantellated 5-orthoplex
Orthogonal projection in BC5 Coxeter plane [10] symmetry
Type	Uniform 5-polytope
Schläfli symbol	t0,2{3,3,3,4}
Coxeter-Dynkin diagram
4-faces	122
Cells	680
Faces	1520
Edges	1280
Vertices	320
Vertex figure
Coxeter group	BC5 [4,3,3,3]
Properties	convex

In five-dimensional geometry, a cantellated 5-orthoplex (or cantellated pentacross) is a uniform 5-polytope.

Alternate names

• Cantellated 5-orthoplex
• Small rhombated triacontiditeron (Acronym: sart) (Jonathan Bowers)

The vertices of the can be made in 5-space, as permutations and sign combinations of:

(0,0,1,1,2)

Images

The cantellated 5-orthoplex is constructed by a cantellation operation applied to the 5-orthoplex.

orthographic projections

Coxeter plane	B5	B4 / D5	B3 / D4 / A2
Graph
Dihedral symmetry	[10]	[8]	[6]
Coxeter plane	B2	A3
Graph
Dihedral symmetry	[4]	[4]

Related polytopes

This polytope is one of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.

B5 polytopes
β5	t1β5	t2γ5	t1γ5	γ5	t0,1β5	t0,2β5	t1,2β5
t0,3β5	t1,3γ5	t1,2γ5	t0,4γ5	t0,3γ5	t0,2γ5	t0,1γ5	t0,1,2β5
t0,1,3β5	t0,2,3β5	t1,2,3γ5	t0,1,4β5	t0,2,4γ5	t0,2,3γ5	t0,1,4γ5	t0,1,3γ5
t0,1,2γ5	t0,1,2,3β5	t0,1,2,4β5	t0,1,3,4γ5	t0,1,2,4γ5	t0,1,2,3γ5	t0,1,2,3,4γ5

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 x3o3x3o4o - sart

External links

• Glossary for hyperspace, George Olshevsky.
• Polytopes of Various Dimensions, Jonathan Bowers
  • Runcinated uniform polytera (spid), Jonathan Bowers
• Multi-dimensional Glossary