D8 polytope
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 8-demicube     =   |
 8-orthoplex   = |
In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, of which 64 are unique and 127 are shared with the B8 symmetry. There is one regular form, the 8-orthoplex with 16 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D8 Coxeter group, and other subgroups.
Graphs
[edit]Symmetric orthographic projections of these 64 polytopes can be made in the D8, D7, D6, D5, D4, D3, A7, 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.
Each of these 64 polytopes is shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position in progressive order: red, orange, yellow, green, cyan, blue, purple, magenta, red-violet.
| # | Coxeter plane graphs | Coxeter diagram Name | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B8 [16/2] | D8 [14] | D7 [12] | D6 [10] | D5 [8] | D4 [6] | D3 [4] | A7 [8] | A5 [6] | A3 [4] | ||
| 1 |  | |  |  |  |  |  |  |  |  |
= 8-demicube |
| 2 |  |  |  |  |  |  |  |  |  |  |
= Cantic 8-cube |
| 3 |  |  |  |  |  |  |  |  |  |  |
= Runcic 8-cube |
| 4 |  |  |  |  |  |  |  |  |  |  |
= Steric 8-cube |
| 5 |  |  |  |  |  |  |  |  |  |  |
= Pentic 8-cube |
| 6 |  |  |  |  |  |  |  |  |  |  |
= Hexic 8-cube |
| 7 |  |  |  |  |  |  |  |  |  |  |
= Heptic 8-cube |
| 8 |  |  |  |  |  |  |  |  |  |  |
= Runcicantic 8-cube |
| 9 |  |  |  |  |  |  |  |  |  |
= Stericantic 8-cube | |
| 10 |  |  |  |  |  |  |  |  |  |
= Steriruncic 8-cube | |
| 11 |  |  |  |  |  |  |  |  |  |  |
= Penticantic 8-cube |
| 12 |  |  |  |  |  |  |  |  |  |
= Pentiruncic 8-cube | |
| 13 |  |  |  |  |  |  |  |  |  |
= Pentisteric 8-cube | |
| 14 |  |  |  |  |  |  |  |  |  |
= Hexicantic 8-cube | |
| 15 |  |  |  |  |  |  |  |  |  |
= Hexiruncic 8-cube | |
| 16 |  |  |  |  |  |  |  |  |  |
= Hexisteric | |
| 17 |  |  |  |  |  |  |  |  |  |
= Hexipentic 8-cube | |
| 18 |  |  |  |  |  |  |  |  |  |
= Hepticantic 8-cube | |
| 19 |  |  |  |  |  |  |  |  |  |
= Heptiruncic 8-cube | |
| 20 |  |  |  |  |  |  |  |  |  |
= Heptisteric 8-cube | |
| 21 |  |  |  |  |  |  |  |  |  |
= Heptipentic 8-cube | |
| 22 |  |  |  |  |  |  |  |  |  |  |
= Heptihexic 8-cube |
| 23 |  |  |  |  |  |  |  |  |  |
= Steriruncicantic 8-cube | |
| 24 |  |  |  |  |  |  |  |  |
= Pentiruncicantic 8-cube | ||
| 25 |  |  |  |  |  |  |  |  |
= Pentistericantic 8-cube | ||
| 26 |  |  |  |  |  |  |  |  |
= Pentisteriruncic 8-cube | ||
| 27 |  |  |  |  |  |  |  |  |
= Hexiruncicantic 8-cube | ||
| 28 |  |  |  |  |  |  |  |  |
= Hexistericantic 8-cube | ||
| 29 |  |  |  |  |  |  |  |  |
= Hexisteriruncic 8-cube | ||
| 30 |  |  |  |  |  |  |  |  |
= Hexipenticantic 8-cube | ||
| 31 |  |  |  |  |  |  |  |  |
= Hexipentiruncic 8-cube | ||
| 32 |  |  |  |  |  |  |  |  |  |
= Hexipentisteric 8-cube | |
| 33 |  |  |  |  |  |  |  |  |  |
= Heptiruncicantic 8-cube | |
| 34 |  |  |  |  |  |  |  |  |
= Heptistericantic 8-cube | ||
| 35 |  |  |  |  |  |  |  |  |  |
= Heptisteriruncic 8-cube | |
| 36 |  |  |  |  |  |  |  |  |
= Heptipenticantic 8-cube | ||
| 37 |  |  |  |  |  |  |  |  |
= Heptipentiruncic 8-cube | ||
| 38 |  |  |  |  |  |  |  |  |  |
= Heptipentisteric 8-cube | |
| 39 |  |  |  |  |  |  |  |  |  |
= Heptihexicantic 8-cube | |
| 40 |  |  |  |  |  |  |  |  |  |
= Heptihexiruncic 8-cube | |
| 41 |  |  |  |  |  |  |  |  |  |
= Heptihexisteric 8-cube | |
| 42 |  |  |  |  |  |  |  |  |  |
= Heptihexipentic 8-cube | |
| 43 |  |  |  |  |  |  |  |  |
= Pentisteriruncicantic 8-cube | ||
| 44 |  |  |  |  |  |  |  |  |
= Hexisteriruncicantic 8-cube | ||
| 45 |  |  |  |  |  |  |  |  |
= Hexipentiruncicantic 8-cube | ||
| 46 |  |  |  |  |  |  |  |  |
= Hexipentistericantic 8-cube | ||
| 47 |  |  |  |  |  |  |  |  |
= Hexipentisteriruncic 8-cube | ||
| 48 |  |  |  |  |  |  |  |  |
= Heptisteriruncicantic 8-cube | ||
| 49 |  |  |  |  |  |  |  |  |
= Heptipentiruncicantic 8-cube | ||
| 50 |  |  |  |  |  |  |  |  |
= Heptipentistericantic 8-cube | ||
| 51 |  |  |  |  |  |  |  |  |
= Heptipentisteriruncic 8-cube | ||
| 52 |  |  |  |  |  |  |  |  |
= Heptihexiruncicantic 8-cube | ||
| 53 |  |  |  |  |  |  |  |  |
= Heptihexistericantic 8-cube | ||
| 54 |  |  |  |  |  |  |  |  |
= Heptihexisteriruncic 8-cube | ||
| 55 |  |  |  |  |  |  |  |  |
= Heptihexipenticantic 8-cube | ||
| 56 |  |  |  |  |  |  |  |  |
= Heptihexipentiruncic 8-cube | ||
| 57 |  |  |  |  |  |  |  |  |
= Heptihexipentisteric 8-cube | ||
| 58 |  |  |  |  |  |  |  |  |
= Hexipentisteriruncicantic 8-cube | ||
| 59 |  |  |  |  |  |  |  |  |
= Heptipentisteriruncicantic 8-cube | ||
| 60 |  |  |  |  |  |  |  |  |
= Heptihexisteriruncicantic 8-cube | ||
| 61 |  |  |  |  |  |  |  |  |
= Heptihexipentiruncicantic 8-cube | ||
| 62 |  |  |  |  |  |  |  |  |
= Heptihexipentistericantic 8-cube | ||
| 63 |  |  |  |  |  |  |  |  |
= Heptihexipentisteriruncic 8-cube | ||
| 64 |  |  |  |  |  |  |  |  |
= Heptihexipentisteriruncicantic 8-cube | ||