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 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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4 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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5 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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6 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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7 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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8 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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9 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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10 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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11 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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12 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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13 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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14 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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15 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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16 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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17 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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18 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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19 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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20 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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21 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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22 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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23 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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24 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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25 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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26 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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27 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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28 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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29 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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30 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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31 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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32 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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33 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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34 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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35 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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36 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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37 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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38 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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39 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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40 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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41 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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42 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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43 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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44 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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45 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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46 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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47 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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48 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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49 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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50 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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51 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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52 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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53 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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54 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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55 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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56 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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57 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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58 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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59 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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60 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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61 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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62 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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63 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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64 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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References
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 | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform 4-polytope | 5-cell | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds |