A5 polytope

Orthographic projections
A5 Coxeter plane

5-simplex

In 5-dimensional geometry, there are 19 uniform polytopes with A5 symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A5 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 19 polytopes can be made in the A5, A4, A3, A2 Coxeter planes. Ak graphs have [k+1] symmetry. For even k and symmetrically nodea_1ed-diagrams, symmetry doubles to [2(k+1)].

These 19 polytopes are each shown in these 4 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

# Coxeter plane graphs Coxeter-Dynkin diagram
Schläfli symbol
Name
[6] [5] [4] [3]
A5 A4 A3 A2
1
{3,3,3,3}
5-simplex (hix)
2
t1{3,3,3,3} or r{3,3,3,3}
Rectified 5-simplex (rix)
3
t2{3,3,3,3} or 2r{3,3,3,3}
Birectified 5-simplex (dot)
4
t0,1{3,3,3,3} or t{3,3,3,3}
Truncated 5-simplex (tix)
5
t1,2{3,3,3,3} or 2t{3,3,3,3}
Bitruncated 5-simplex (bittix)
6
t0,2{3,3,3,3} or rr{3,3,3,3}
Cantellated 5-simplex (sarx)
7
t1,3{3,3,3,3} or 2rr{3,3,3,3}
Bicantellated 5-simplex (sibrid)
8
t0,3{3,3,3,3}
Runcinated 5-simplex (spix)
9
t0,4{3,3,3,3} or 2r2r{3,3,3,3}
Stericated 5-simplex (scad)
10
t0,1,2{3,3,3,3} or tr{3,3,3,3}
Cantitruncated 5-simplex (garx)
11
t1,2,3{3,3,3,3} or 2tr{3,3,3,3}
Bicantitruncated 5-simplex (gibrid)
12
t0,1,3{3,3,3,3}
Runcitruncated 5-simplex (pattix)
13
t0,2,3{3,3,3,3}
Runcicantellated 5-simplex (pirx)
14
t0,1,4{3,3,3,3}
Steritruncated 5-simplex (cappix)
15
t0,2,4{3,3,3,3}
Stericantellated 5-simplex (card)
16
t0,1,2,3{3,3,3,3}
Runcicantitruncated 5-simplex (gippix)
17
t0,1,2,4{3,3,3,3}
Stericantitruncated 5-simplex (cograx)
18
t0,1,3,4{3,3,3,3}
Steriruncitruncated 5-simplex (captid)
19
t0,1,2,3,4{3,3,3,3}
Omnitruncated 5-simplex (gocad)

References

External links

Notes

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds
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