# D8 polytope

 8-demicube = 8-orthoplex =

In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, 64 are unique, and 127 are shared with the B8 symmetry. There are two regular forms, the 8-orthoplex, and 8-demicube with 16 and 128 vertices respectively.

They can be visualized as symmetric orthographic projections in Coxeter planes of the D8 Coxeter group, and other subgroups.

## Graphs

Symmetric orthographic projections of these 64 polytopes can be made in the D8, D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B8 is also included although only half of its [16] symmetry exists in these polytopes.

These 64 polytopes are each shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

# Coxeter plane graphs Coxeter diagram
Names
B8
[16/2]
D8
[14]
D7
[12]
D6
[10]
D5
[8]
D4
[6]
D3
[4]
A7
[8]
A5
[6]
A3
[4]
1 =
8-demicube (hocto)
2 =
Truncated 8-demicube (thocto)
3 =
4 =
5 =
6 =
7 =
8 =
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64   =

## References

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / 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