# D8 polytope

Orthographic projections in the D$_8$ Coxeter plane :
| 8-demicube = | 8-orthoplex = |
In 8-dimensional geometry, there are 191 uniform polytopes with D$_8$ symmetry, 64 are unique, and 127 are shared with the B$_8$ 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 D$_8$ Coxeter group, and other subgroups.

## Graphs

Symmetric orthographic projections of these 64 polytopes can be made in the D$_8$, D$_7$, D$_6$, D$_5$, D$_4$, D$_3$, A$_5$, A$_3$, Coxeter planes. A$_k$ has [k+1] symmetry, D$_k$ has [2(k-1)] symmetry. B$_8$ 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 plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter diagram Names |
| # | B$_8$ [16/2] | D$_8$ [14] | D$_7$ [12] | D$_6$ [10] | D$_5$ [8] | D$_4$ [6] | D$_3$ [4] | A$_7$ [8] | A$_5$ [6] | A$_3$ [4] | Coxeter diagram Names |
| 1 | | | | | | | | | | | = 8-demicube (hocto) |
| 2 | | | | | | | | | | | = cantic 8-cube (thocto) |
| 3 | | | | | | | | | | | = runcic 8-cube |
| 4 | | | | | | | | | | | = steric 8-cube |
| 5 | | | | | | | | | | | = pentic 8-cube |
| 6 | | | | | | | | | | | = hexic 8-cube |
| 7 | | | | | | | | | | | = heptic 8-cube |
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