A8 polytope
![]() 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
In 8-dimensional geometry, there are 135 uniform polytopes with A8 symmetry. There is one self-dual regular form, the 8-simplex with 9 vertices.
Each can be visualized as symmetric orthographic projections in Coxeter planes of the A8 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 135 polytopes can be made in the A8, A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry.
These 135 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
# | Coxeter-Dynkin diagram Schläfli symbol Johnson name |
Ak orthogonal projection graphs | ||||||
---|---|---|---|---|---|---|---|---|
A8 [9] |
A7 [8] |
A6 [7] |
A5 [6] |
A4 [5] |
A3 [4] |
A2 [3] | ||
1 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0{3,3,3,3,3,3,3} 8-simplex |
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2 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1{3,3,3,3,3,3,3} Rectified 8-simplex |
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3 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2{3,3,3,3,3,3,3} Birectified 8-simplex |
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4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t3{3,3,3,3,3,3,3} Trirectified 8-simplex |
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5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1{3,3,3,3,3,3,3} Truncated 8-simplex |
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6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2{3,3,3,3,3,3,3} Cantellated 8-simplex |
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7 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2{3,3,3,3,3,3,3} Bitruncated 8-simplex |
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8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3{3,3,3,3,3,3,3} Runcinated 8-simplex |
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9 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3{3,3,3,3,3,3,3} Bicantellated 8-simplex |
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10 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,3{3,3,3,3,3,3,3} Tritruncated 8-simplex |
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11 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,4{3,3,3,3,3,3,3} Stericated 8-simplex |
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12 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,4{3,3,3,3,3,3,3} Biruncinated 8-simplex |
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13 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,4{3,3,3,3,3,3,3} Tricantellated 8-simplex |
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14 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t3,4{3,3,3,3,3,3,3} Quadritruncated 8-simplex |
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15 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,5{3,3,3,3,3,3,3} Pentellated 8-simplex |
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16 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,5{3,3,3,3,3,3,3} Bistericated 8-simplex |
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17 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,5{3,3,3,3,3,3,3} Triruncinated 8-simplex |
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18 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,6{3,3,3,3,3,3,3} Hexicated 8-simplex |
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19 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,6{3,3,3,3,3,3,3} Bipentellated 8-simplex |
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20 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,7{3,3,3,3,3,3,3} Heptellated 8-simplex |
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21 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2{3,3,3,3,3,3,3} Cantitruncated 8-simplex |
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22 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3{3,3,3,3,3,3,3} Runcitruncated 8-simplex |
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23 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3{3,3,3,3,3,3,3} Runcicantellated 8-simplex |
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24 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3{3,3,3,3,3,3,3} Bicantitruncated 8-simplex |
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25 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4{3,3,3,3,3,3,3} Steritruncated 8-simplex |
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26 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,4{3,3,3,3,3,3,3} Stericantellated 8-simplex |
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27 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,4{3,3,3,3,3,3,3} Biruncitruncated 8-simplex |
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28 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,4{3,3,3,3,3,3,3} Steriruncinated 8-simplex |
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29 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3,4{3,3,3,3,3,3,3} Biruncicantellated 8-simplex |
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30 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,3,4{3,3,3,3,3,3,3} Tricantitruncated 8-simplex |
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31 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,5{3,3,3,3,3,3,3} Pentitruncated 8-simplex |
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32 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,5{3,3,3,3,3,3,3} Penticantellated 8-simplex |
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33 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,5{3,3,3,3,3,3,3} Bisteritruncated 8-simplex |
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34 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,5{3,3,3,3,3,3,3} Pentiruncinated 8-simplex |
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35 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3,5{3,3,3,3,3,3,3} Bistericantellated 8-simplex |
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36 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,3,5{3,3,3,3,3,3,3} Triruncitruncated 8-simplex |
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37 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,4,5{3,3,3,3,3,3,3} Pentistericated 8-simplex |
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38 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,4,5{3,3,3,3,3,3,3} Bisteriruncinated 8-simplex |
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39 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,6{3,3,3,3,3,3,3} Hexitruncated 8-simplex |
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40 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,6{3,3,3,3,3,3,3} Hexicantellated 8-simplex |
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41 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,6{3,3,3,3,3,3,3} Bipentitruncated 8-simplex |
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42 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,6{3,3,3,3,3,3,3} Hexiruncinated 8-simplex |
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43 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3,6{3,3,3,3,3,3,3} Bipenticantellated 8-simplex |
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44 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,4,6{3,3,3,3,3,3,3} Hexistericated 8-simplex |
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45 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,5,6{3,3,3,3,3,3,3} Hexipentellated 8-simplex |
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46 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,7{3,3,3,3,3,3,3} Heptitruncated 8-simplex |
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47 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,7{3,3,3,3,3,3,3} Hepticantellated 8-simplex |
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48 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,7{3,3,3,3,3,3,3} Heptiruncinated 8-simplex |
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49 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3{3,3,3,3,3,3,3} Runcicantitruncated 8-simplex |
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50 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4{3,3,3,3,3,3,3} Stericantitruncated 8-simplex |
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51 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4{3,3,3,3,3,3,3} Steriruncitruncated 8-simplex |
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52 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4{3,3,3,3,3,3,3} Steriruncicantellated 8-simplex |
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53 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,4{3,3,3,3,3,3,3} Biruncicantitruncated 8-simplex |
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54 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,5{3,3,3,3,3,3,3} Penticantitruncated 8-simplex |
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55 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,5{3,3,3,3,3,3,3} Pentiruncitruncated 8-simplex |
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56 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,5{3,3,3,3,3,3,3} Pentiruncicantellated 8-simplex |
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57 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,5{3,3,3,3,3,3,3} Bistericantitruncated 8-simplex |
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58 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4,5{3,3,3,3,3,3,3} Pentisteritruncated 8-simplex |
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59 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,4,5{3,3,3,3,3,3,3} Pentistericantellated 8-simplex |
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60 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,4,5{3,3,3,3,3,3,3} Bisteriruncitruncated 8-simplex |
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61 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,4,5{3,3,3,3,3,3,3} Pentisteriruncinated 8-simplex |
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62 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3,4,5{3,3,3,3,3,3,3} Bisteriruncicantellated 8-simplex |
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63 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t2,3,4,5{3,3,3,3,3,3,3} Triruncicantitruncated 8-simplex |
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64 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,6{3,3,3,3,3,3,3} Hexicantitruncated 8-simplex |
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65 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,6{3,3,3,3,3,3,3} Hexiruncitruncated 8-simplex |
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66 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,6{3,3,3,3,3,3,3} Hexiruncicantellated 8-simplex |
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67 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,6{3,3,3,3,3,3,3} Bipenticantitruncated 8-simplex |
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68 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4,6{3,3,3,3,3,3,3} Hexisteritruncated 8-simplex |
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69 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,4,6{3,3,3,3,3,3,3} Hexistericantellated 8-simplex |
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70 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,4,6{3,3,3,3,3,3,3} Bipentiruncitruncated 8-simplex |
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71 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,4,6{3,3,3,3,3,3,3} Hexisteriruncinated 8-simplex |
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72 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,3,4,6{3,3,3,3,3,3,3} Bipentiruncicantellated 8-simplex |
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73 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,5,6{3,3,3,3,3,3,3} Hexipentitruncated 8-simplex |
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74 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,5,6{3,3,3,3,3,3,3} Hexipenticantellated 8-simplex |
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75 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,5,6{3,3,3,3,3,3,3} Bipentisteritruncated 8-simplex |
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76 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,5,6{3,3,3,3,3,3,3} Hexipentiruncinated 8-simplex |
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77 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,4,5,6{3,3,3,3,3,3,3} Hexipentistericated 8-simplex |
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78 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,7{3,3,3,3,3,3,3} Hepticantitruncated 8-simplex |
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79 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,7{3,3,3,3,3,3,3} Heptiruncitruncated 8-simplex |
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80 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,7{3,3,3,3,3,3,3} Heptiruncicantellated 8-simplex |
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81 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4,7{3,3,3,3,3,3,3} Heptisteritruncated 8-simplex |
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82 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,4,7{3,3,3,3,3,3,3} Heptistericantellated 8-simplex |
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83 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,4,7{3,3,3,3,3,3,3} Heptisteriruncinated 8-simplex |
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84 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,5,7{3,3,3,3,3,3,3} Heptipentitruncated 8-simplex |
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85 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,5,7{3,3,3,3,3,3,3} Heptipenticantellated 8-simplex |
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86 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,6,7{3,3,3,3,3,3,3} Heptihexitruncated 8-simplex |
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87 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4{3,3,3,3,3,3,3} Steriruncicantitruncated 8-simplex |
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88 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,5{3,3,3,3,3,3,3} Pentiruncicantitruncated 8-simplex |
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89 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,5{3,3,3,3,3,3,3} Pentistericantitruncated 8-simplex |
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90 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,5{3,3,3,3,3,3,3} Pentisteriruncitruncated 8-simplex |
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91 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4,5{3,3,3,3,3,3,3} Pentisteriruncicantellated 8-simplex |
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92 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,4,5{3,3,3,3,3,3,3} Bisteriruncicantitruncated 8-simplex |
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93 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,6{3,3,3,3,3,3,3} Hexiruncicantitruncated 8-simplex |
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94 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,6{3,3,3,3,3,3,3} Hexistericantitruncated 8-simplex |
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95 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,6{3,3,3,3,3,3,3} Hexisteriruncitruncated 8-simplex |
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96 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4,6{3,3,3,3,3,3,3} Hexisteriruncicantellated 8-simplex |
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97 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,4,6{3,3,3,3,3,3,3} Bipentiruncicantitruncated 8-simplex |
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98 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,5,6{3,3,3,3,3,3,3} Hexipenticantitruncated 8-simplex |
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99 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,5,6{3,3,3,3,3,3,3} Hexipentiruncitruncated 8-simplex |
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100 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,5,6{3,3,3,3,3,3,3} Hexipentiruncicantellated 8-simplex |
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101 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,5,6{3,3,3,3,3,3,3} Bipentistericantitruncated 8-simplex |
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102 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4,5,6{3,3,3,3,3,3,3} Hexipentisteritruncated 8-simplex |
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103 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,4,5,6{3,3,3,3,3,3,3} Hexipentistericantellated 8-simplex |
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104 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,3,4,5,6{3,3,3,3,3,3,3} Hexipentisteriruncinated 8-simplex |
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105 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,7{3,3,3,3,3,3,3} Heptiruncicantitruncated 8-simplex |
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106 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,7{3,3,3,3,3,3,3} Heptistericantitruncated 8-simplex |
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107 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,7{3,3,3,3,3,3,3} Heptisteriruncitruncated 8-simplex |
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108 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4,7{3,3,3,3,3,3,3} Heptisteriruncicantellated 8-simplex |
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109 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,5,7{3,3,3,3,3,3,3} Heptipenticantitruncated 8-simplex |
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110 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,5,7{3,3,3,3,3,3,3} Heptipentiruncitruncated 8-simplex |
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111 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,5,7{3,3,3,3,3,3,3} Heptipentiruncicantellated 8-simplex |
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112 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,4,5,7{3,3,3,3,3,3,3} Heptipentisteritruncated 8-simplex |
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113 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,6,7{3,3,3,3,3,3,3} Heptihexicantitruncated 8-simplex |
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114 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,6,7{3,3,3,3,3,3,3} Heptihexiruncitruncated 8-simplex |
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115 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,5{3,3,3,3,3,3,3} Pentisteriruncicantitruncated 8-simplex |
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116 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,6{3,3,3,3,3,3,3} Hexisteriruncicantitruncated 8-simplex |
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117 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,5,6{3,3,3,3,3,3,3} Hexipentiruncicantitruncated 8-simplex |
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118 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,5,6{3,3,3,3,3,3,3} Hexipentistericantitruncated 8-simplex |
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119 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,5,6{3,3,3,3,3,3,3} Hexipentisteriruncitruncated 8-simplex |
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120 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4,5,6{3,3,3,3,3,3,3} Hexipentisteriruncicantellated 8-simplex |
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121 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t1,2,3,4,5,6{3,3,3,3,3,3,3} Bipentisteriruncicantitruncated 8-simplex |
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122 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,7{3,3,3,3,3,3,3} Heptisteriruncicantitruncated 8-simplex |
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123 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,5,7{3,3,3,3,3,3,3} Heptipentiruncicantitruncated 8-simplex |
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124 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,5,7{3,3,3,3,3,3,3} Heptipentistericantitruncated 8-simplex |
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125 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,5,7{3,3,3,3,3,3,3} Heptipentisteriruncitruncated 8-simplex |
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126 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,2,3,4,5,7{3,3,3,3,3,3,3} Heptipentisteriruncicantellated 8-simplex |
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127 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,6,7{3,3,3,3,3,3,3} Heptihexiruncicantitruncated 8-simplex |
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128 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,4,6,7{3,3,3,3,3,3,3} Heptihexistericantitruncated 8-simplex |
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129 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,3,4,6,7{3,3,3,3,3,3,3} Heptihexisteriruncitruncated 8-simplex |
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130 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,5,6,7{3,3,3,3,3,3,3} Heptihexipenticantitruncated 8-simplex |
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131 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,5,6{3,3,3,3,3,3,3} Hexipentisteriruncicantitruncated 8-simplex |
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132 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,5,7{3,3,3,3,3,3,3} Heptipentisteriruncicantitruncated 8-simplex |
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133 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,6,7{3,3,3,3,3,3,3} Heptihexisteriruncicantitruncated 8-simplex |
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134 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,5,6,7{3,3,3,3,3,3,3} Heptihexipentiruncicantitruncated 8-simplex |
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135 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() t0,1,2,3,4,5,6,7{3,3,3,3,3,3,3} Omnitruncated 8-simplex |
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References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
- Klitzing, Richard. "8D uniform polytopes (polyzetta)".
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 | 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 |
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