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Coxeter-Dynkin diagram
Schläfli symbol
Johnson name
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Ak
orthogonal projection graphs
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A7 [8]
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A6 [7]
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A5 [6]
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A4 [5]
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A3 [4]
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A2 [3]
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1
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t0{3,3,3,3,3,3}
7-simplex
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2
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t1{3,3,3,3,3,3}
Rectified 7-simplex
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3
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t2{3,3,3,3,3,3}
Birectified 7-simplex
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4
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t3{3,3,3,3,3,3}
Trirectified 7-simplex
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5
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t0,1{3,3,3,3,3,3}
Truncated 7-simplex
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6
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t0,2{3,3,3,3,3,3}
Cantellated 7-simplex
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7
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t1,2{3,3,3,3,3,3}
Bitruncated 7-simplex
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8
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t0,3{3,3,3,3,3,3}
Runcinated 7-simplex
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9
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t1,3{3,3,3,3,3,3}
Bicantellated 7-simplex
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10
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t2,3{3,3,3,3,3,3}
Tritruncated 7-simplex
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11
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t0,4{3,3,3,3,3,3}
Stericated 7-simplex
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12
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t1,4{3,3,3,3,3,3}
Biruncinated 7-simplex
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13
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t2,4{3,3,3,3,3,3}
Tricantellated 7-simplex
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14
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t0,5{3,3,3,3,3,3}
Pentellated 7-simplex
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15
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t1,5{3,3,3,3,3,3}
Bistericated 7-simplex
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16
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t0,6{3,3,3,3,3,3}
Hexicated 7-simplex
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17
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t0,1,2{3,3,3,3,3,3}
Cantitruncated 7-simplex
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18
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t0,1,3{3,3,3,3,3,3}
Runcitruncated 7-simplex
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19
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t0,2,3{3,3,3,3,3,3}
Runcicantellated 7-simplex
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20
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t1,2,3{3,3,3,3,3,3}
Bicantitruncated 7-simplex
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21
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t0,1,4{3,3,3,3,3,3}
Steritruncated 7-simplex
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22
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t0,2,4{3,3,3,3,3,3}
Stericantellated 7-simplex
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23
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t1,2,4{3,3,3,3,3,3}
Biruncitruncated 7-simplex
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24
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t0,3,4{3,3,3,3,3,3}
Steriruncinated 7-simplex
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25
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t1,3,4{3,3,3,3,3,3}
Biruncicantellated 7-simplex
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26
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t2,3,4{3,3,3,3,3,3}
Tricantitruncated 7-simplex
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27
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t0,1,5{3,3,3,3,3,3}
Pentitruncated 7-simplex
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28
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t0,2,5{3,3,3,3,3,3}
Penticantellated 7-simplex
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29
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t1,2,5{3,3,3,3,3,3}
Bisteritruncated 7-simplex
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30
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t0,3,5{3,3,3,3,3,3}
Pentiruncinated 7-simplex
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31
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t1,3,5{3,3,3,3,3,3}
Bistericantellated 7-simplex
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32
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t0,4,5{3,3,3,3,3,3}
Pentistericated 7-simplex
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33
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t0,1,6{3,3,3,3,3,3}
Hexitruncated 7-simplex
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34
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t0,2,6{3,3,3,3,3,3}
Hexicantellated 7-simplex
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35
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t0,3,6{3,3,3,3,3,3}
Hexiruncinated 7-simplex
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36
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t0,1,2,3{3,3,3,3,3,3}
Runcicantitruncated 7-simplex
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37
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t0,1,2,4{3,3,3,3,3,3}
Stericantitruncated 7-simplex
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38
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t0,1,3,4{3,3,3,3,3,3}
Steriruncitruncated 7-simplex
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39
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t0,2,3,4{3,3,3,3,3,3}
Steriruncicantellated 7-simplex
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40
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t1,2,3,4{3,3,3,3,3,3}
Biruncicantitruncated 7-simplex
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41
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t0,1,2,5{3,3,3,3,3,3}
Penticantitruncated 7-simplex
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42
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t0,1,3,5{3,3,3,3,3,3}
Pentiruncitruncated 7-simplex
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43
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t0,2,3,5{3,3,3,3,3,3}
Pentiruncicantellated 7-simplex
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44
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t1,2,3,5{3,3,3,3,3,3}
Bistericantitruncated 7-simplex
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45
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t0,1,4,5{3,3,3,3,3,3}
Pentisteritruncated 7-simplex
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46
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t0,2,4,5{3,3,3,3,3,3}
Pentistericantellated 7-simplex
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47
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t1,2,4,5{3,3,3,3,3,3}
Bisteriruncitruncated 7-simplex
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48
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t0,3,4,5{3,3,3,3,3,3}
Pentisteriruncinated 7-simplex
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49
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t0,1,2,6{3,3,3,3,3,3}
Hexicantitruncated 7-simplex
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50
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t0,1,3,6{3,3,3,3,3,3}
Hexiruncitruncated 7-simplex
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51
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t0,2,3,6{3,3,3,3,3,3}
Hexiruncicantellated 7-simplex
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52
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t0,1,4,6{3,3,3,3,3,3}
Hexisteritruncated 7-simplex
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53
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t0,2,4,6{3,3,3,3,3,3}
Hexistericantellated 7-simplex
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54
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t0,1,5,6{3,3,3,3,3,3}
Hexipentitruncated 7-simplex
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55
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t0,1,2,3,4{3,3,3,3,3,3}
Steriruncicantitruncated 7-simplex
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56
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t0,1,2,3,5{3,3,3,3,3,3}
Pentiruncicantitruncated 7-simplex
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57
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t0,1,2,4,5{3,3,3,3,3,3}
Pentistericantitruncated 7-simplex
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58
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t0,1,3,4,5{3,3,3,3,3,3}
Pentisteriruncitruncated 7-simplex
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59
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t0,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantellated 7-simplex
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60
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t1,2,3,4,5{3,3,3,3,3,3}
Bisteriruncicantitruncated 7-simplex
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61
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t0,1,2,3,6{3,3,3,3,3,3}
Hexiruncicantitruncated 7-simplex
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62
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t0,1,2,4,6{3,3,3,3,3,3}
Hexistericantitruncated 7-simplex
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63
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t0,1,3,4,6{3,3,3,3,3,3}
Hexisteriruncitruncated 7-simplex
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64
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t0,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantellated 7-simplex
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65
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t0,1,2,5,6{3,3,3,3,3,3}
Hexipenticantitruncated 7-simplex
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66
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t0,1,3,5,6{3,3,3,3,3,3}
Hexipentiruncitruncated 7-simplex
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67
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t0,1,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantitruncated 7-simplex
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68
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t0,1,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantitruncated 7-simplex
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69
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t0,1,2,3,5,6{3,3,3,3,3,3}
Hexipentiruncicantitruncated 7-simplex
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70
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t0,1,2,4,5,6{3,3,3,3,3,3}
Hexipentistericantitruncated 7-simplex
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71
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t0,1,2,3,4,5,6{3,3,3,3,3,3}
Omnitruncated 7-simplex
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