In 8dimensional geometry, there are 256 uniform polytopes with B8 symmetry. There are two regular forms, the 8orthoplex, and 8cube with 16 and 256 vertices respectively. The 8demicube is added with half the symmetry.
They can be visualized as symmetric orthographic projections in Coxeter planes of the B8 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.
These 256 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.
Element counts  CoxeterDynkin diagram Schläfli symbol Name 


B_{8} [16] 
B_{7} [14] 
B_{6} [12] 
B_{5} [10] 
B_{4} [8] 
B_{3} [6] 
B_{2} [4] 
A_{7} [8] 
A_{5} [6] 
A_{3} [4] 

1  t_{0}{3,3,3,3,3,3,4} 8orthoplex Diacosipentacontahexazetton (ek) 

2  t_{1}{3,3,3,3,3,3,4} Rectified 8orthoplex Rectified diacosipentacontahexazetton (rek) 

3  t_{2}{3,3,3,3,3,3,4} Birectified 8orthoplex Birectified diacosipentacontahexazetton (bark) 

4  t_{3}{3,3,3,3,3,3,4} Trirectified 8orthoplex Trirectified diacosipentacontahexazetton (tark) 

5  t_{3}{4,3,3,3,3,3,3} Trirectified 8cube Trirectified octeract (tro) 

6  t_{2}{4,3,3,3,3,3,3} Birectified 8cube Birectified octeract (bro) 

7  t_{1}{4,3,3,3,3,3,3} Rectified 8cube Rectified octeract (recto) 

8  t_{0}{4,3,3,3,3,3,3} 8cube Octeract (octo) 

9  t_{0,1}{3,3,3,3,3,3,4} Truncated 8orthoplex Truncated diacosipentacontahexazetton (tek) 

10  t_{0,2}{3,3,3,3,3,3,4} Cantellated 8orthoplex Small rhombated diacosipentacontahexazetton (srek) 

11  t_{1,2}{3,3,3,3,3,3,4} Bitruncated 8orthoplex Bitruncated diacosipentacontahexazetton (batek) 

12  t_{0,3}{3,3,3,3,3,3,4} Runcinated 8orthoplex Small prismated diacosipentacontahexazetton (spek) 

13  t_{1,3}{3,3,3,3,3,3,4} Bicantellated 8orthoplex Small birhombated diacosipentacontahexazetton (sabork) 

14  t_{2,3}{3,3,3,3,3,3,4} Tritruncated 8orthoplex Tritruncated diacosipentacontahexazetton (tatek) 

15  t_{0,4}{3,3,3,3,3,3,4} Stericated 8orthoplex Small cellated diacosipentacontahexazetton (scak) 

16  t_{1,4}{3,3,3,3,3,3,4} Biruncinated 8orthoplex Small biprismated diacosipentacontahexazetton (sabpek) 

17  t_{2,4}{3,3,3,3,3,3,4} Tricantellated 8orthoplex Small trirhombated diacosipentacontahexazetton (satrek) 

18  t_{3,4}{4,3,3,3,3,3,3} Quadritruncated 8cube Octeractidiacosipentacontahexazetton (oke) 

19  t_{0,5}{3,3,3,3,3,3,4} Pentellated 8orthoplex Small terated diacosipentacontahexazetton (setek) 

20  t_{1,5}{3,3,3,3,3,3,4} Bistericated 8orthoplex Small bicellated diacosipentacontahexazetton (sibcak) 

21  t_{2,5}{4,3,3,3,3,3,3} Triruncinated 8cube Small triprismatoocteractidiacosipentacontahexazetton (sitpoke) 

22  t_{2,4}{4,3,3,3,3,3,3} Tricantellated 8cube Small trirhombated octeract (satro) 

23  t_{2,3}{4,3,3,3,3,3,3} Tritruncated 8cube Tritruncated octeract (tato) 

24  t_{0,6}{3,3,3,3,3,3,4} Hexicated 8orthoplex Small petated diacosipentacontahexazetton (supek) 

25  t_{1,6}{4,3,3,3,3,3,3} Bipentellated 8cube Small biteriocteractidiacosipentacontahexazetton (sabtoke) 

26  t_{1,5}{4,3,3,3,3,3,3} Bistericated 8cube Small bicellated octeract (sobco) 

27  t_{1,4}{4,3,3,3,3,3,3} Biruncinated 8cube Small biprismated octeract (sabepo) 

28  t_{1,3}{4,3,3,3,3,3,3} Bicantellated 8cube Small birhombated octeract (subro) 

29  t_{1,2}{4,3,3,3,3,3,3} Bitruncated 8cube Bitruncated octeract (bato) 

30  t_{0,7}{4,3,3,3,3,3,3} Heptellated 8cube Small exiocteractidiacosipentacontahexazetton (saxoke) 

31  t_{0,6}{4,3,3,3,3,3,3} Hexicated 8cube Small petated octeract (supo) 

32  t_{0,5}{4,3,3,3,3,3,3} Pentellated 8cube Small terated octeract (soto) 

33  t_{0,4}{4,3,3,3,3,3,3} Stericated 8cube Small cellated octeract (soco) 

34  t_{0,3}{4,3,3,3,3,3,3} Runcinated 8cube Small prismated octeract (sopo) 

35  t_{0,2}{4,3,3,3,3,3,3} Cantellated 8cube Small rhombated octeract (soro) 

36  t_{0,1}{4,3,3,3,3,3,3} Truncated 8cube Truncated octeract (tocto) 

37  t_{0,1,2}{3,3,3,3,3,3,4} Cantitruncated 8orthoplex Great rhombated diacosipentacontahexazetton 

38  t_{0,1,3}{3,3,3,3,3,3,4} Runcitruncated 8orthoplex Prismatotruncated diacosipentacontahexazetton 

39  t_{0,2,3}{3,3,3,3,3,3,4} Runcicantellated 8orthoplex Prismatorhombated diacosipentacontahexazetton 

40  t_{1,2,3}{3,3,3,3,3,3,4} Bicantitruncated 8orthoplex Great birhombated diacosipentacontahexazetton 

41  t_{0,1,4}{3,3,3,3,3,3,4} Steritruncated 8orthoplex Cellitruncated diacosipentacontahexazetton 

42  t_{0,2,4}{3,3,3,3,3,3,4} Stericantellated 8orthoplex Cellirhombated diacosipentacontahexazetton 

43  t_{1,2,4}{3,3,3,3,3,3,4} Biruncitruncated 8orthoplex Biprismatotruncated diacosipentacontahexazetton 

44  t_{0,3,4}{3,3,3,3,3,3,4} Steriruncinated 8orthoplex Celliprismated diacosipentacontahexazetton 

45  t_{1,3,4}{3,3,3,3,3,3,4} Biruncicantellated 8orthoplex Biprismatorhombated diacosipentacontahexazetton 

46  t_{2,3,4}{3,3,3,3,3,3,4} Tricantitruncated 8orthoplex Great trirhombated diacosipentacontahexazetton 

47  t_{0,1,5}{3,3,3,3,3,3,4} Pentitruncated 8orthoplex Teritruncated diacosipentacontahexazetton 

48  t_{0,2,5}{3,3,3,3,3,3,4} Penticantellated 8orthoplex Terirhombated diacosipentacontahexazetton 

49  t_{1,2,5}{3,3,3,3,3,3,4} Bisteritruncated 8orthoplex Bicellitruncated diacosipentacontahexazetton 

50  t_{0,3,5}{3,3,3,3,3,3,4} Pentiruncinated 8orthoplex Teriprismated diacosipentacontahexazetton 

51  t_{1,3,5}{3,3,3,3,3,3,4} Bistericantellated 8orthoplex Bicellirhombated diacosipentacontahexazetton 

52  t_{2,3,5}{3,3,3,3,3,3,4} Triruncitruncated 8orthoplex Triprismatotruncated diacosipentacontahexazetton 

53  t_{0,4,5}{3,3,3,3,3,3,4} Pentistericated 8orthoplex Tericellated diacosipentacontahexazetton 

54  t_{1,4,5}{3,3,3,3,3,3,4} Bisteriruncinated 8orthoplex Bicelliprismated diacosipentacontahexazetton 

55  t_{2,3,5}{4,3,3,3,3,3,3} Triruncitruncated 8cube Triprismatotruncated octeract 

56  t_{2,3,4}{4,3,3,3,3,3,3} Tricantitruncated 8cube Great trirhombated octeract 

57  t_{0,1,6}{3,3,3,3,3,3,4} Hexitruncated 8orthoplex Petitruncated diacosipentacontahexazetton 

58  t_{0,2,6}{3,3,3,3,3,3,4} Hexicantellated 8orthoplex Petirhombated diacosipentacontahexazetton 

59  t_{1,2,6}{3,3,3,3,3,3,4} Bipentitruncated 8orthoplex Biteritruncated diacosipentacontahexazetton 

60  t_{0,3,6}{3,3,3,3,3,3,4} Hexiruncinated 8orthoplex Petiprismated diacosipentacontahexazetton 

61  t_{1,3,6}{3,3,3,3,3,3,4} Bipenticantellated 8orthoplex Biterirhombated diacosipentacontahexazetton 

62  t_{1,4,5}{4,3,3,3,3,3,3} Bisteriruncinated 8cube Bicelliprismated octeract 

63  t_{0,4,6}{3,3,3,3,3,3,4} Hexistericated 8orthoplex Peticellated diacosipentacontahexazetton 

64  t_{1,3,6}{4,3,3,3,3,3,3} Bipenticantellated 8cube Biterirhombated octeract 

65  t_{1,3,5}{4,3,3,3,3,3,3} Bistericantellated 8cube Bicellirhombated octeract 

66  t_{1,3,4}{4,3,3,3,3,3,3} Biruncicantellated 8cube Biprismatorhombated octeract 

67  t_{0,5,6}{3,3,3,3,3,3,4} Hexipentellated 8orthoplex Petiterated diacosipentacontahexazetton 

68  t_{1,2,6}{4,3,3,3,3,3,3} Bipentitruncated 8cube Biteritruncated octeract 

69  t_{1,2,5}{4,3,3,3,3,3,3} Bisteritruncated 8cube Bicellitruncated octeract 

70  t_{1,2,4}{4,3,3,3,3,3,3} Biruncitruncated 8cube Biprismatotruncated octeract 

71  t_{1,2,3}{4,3,3,3,3,3,3} Bicantitruncated 8cube Great birhombated octeract 

72  t_{0,1,7}{3,3,3,3,3,3,4} Heptitruncated 8orthoplex Exitruncated diacosipentacontahexazetton 

73  t_{0,2,7}{3,3,3,3,3,3,4} Hepticantellated 8orthoplex Exirhombated diacosipentacontahexazetton 

74  t_{0,5,6}{4,3,3,3,3,3,3} Hexipentellated 8cube Petiterated octeract 

75  t_{0,3,7}{3,3,3,3,3,3,4} Heptiruncinated 8orthoplex Exiprismated diacosipentacontahexazetton 

76  t_{0,4,6}{4,3,3,3,3,3,3} Hexistericated 8cube Peticellated octeract 

77  t_{0,4,5}{4,3,3,3,3,3,3} Pentistericated 8cube Tericellated octeract 

78  t_{0,3,7}{4,3,3,3,3,3,3} Heptiruncinated 8cube Exiprismated octeract 

79  t_{0,3,6}{4,3,3,3,3,3,3} Hexiruncinated 8cube Petiprismated octeract 

80  t_{0,3,5}{4,3,3,3,3,3,3} Pentiruncinated 8cube Teriprismated octeract 

81  t_{0,3,4}{4,3,3,3,3,3,3} Steriruncinated 8cube Celliprismated octeract 

82  t_{0,2,7}{4,3,3,3,3,3,3} Hepticantellated 8cube Exirhombated octeract 

83  t_{0,2,6}{4,3,3,3,3,3,3} Hexicantellated 8cube Petirhombated octeract 

84  t_{0,2,5}{4,3,3,3,3,3,3} Penticantellated 8cube Terirhombated octeract 

85  t_{0,2,4}{4,3,3,3,3,3,3} Stericantellated 8cube Cellirhombated octeract 

86  t_{0,2,3}{4,3,3,3,3,3,3} Runcicantellated 8cube Prismatorhombated octeract 

87  t_{0,1,7}{4,3,3,3,3,3,3} Heptitruncated 8cube Exitruncated octeract 

88  t_{0,1,6}{4,3,3,3,3,3,3} Hexitruncated 8cube Petitruncated octeract 

89  t_{0,1,5}{4,3,3,3,3,3,3} Pentitruncated 8cube Teritruncated octeract 

90  t_{0,1,4}{4,3,3,3,3,3,3} Steritruncated 8cube Cellitruncated octeract 

91  t_{0,1,3}{4,3,3,3,3,3,3} Runcitruncated 8cube Prismatotruncated octeract 

92  t_{0,1,2}{4,3,3,3,3,3,3} Cantitruncated 8cube Great rhombated octeract 

93  t_{0,1,2,3}{3,3,3,3,3,3,4} Runcicantitruncated 8orthoplex Great prismated diacosipentacontahexazetton 

94  t_{0,1,2,4}{3,3,3,3,3,3,4} Stericantitruncated 8orthoplex Celligreatorhombated diacosipentacontahexazetton 

95  t_{0,1,3,4}{3,3,3,3,3,3,4} Steriruncitruncated 8orthoplex Celliprismatotruncated diacosipentacontahexazetton 

96  t_{0,2,3,4}{3,3,3,3,3,3,4} Steriruncicantellated 8orthoplex Celliprismatorhombated diacosipentacontahexazetton 

97  t_{1,2,3,4}{3,3,3,3,3,3,4} Biruncicantitruncated 8orthoplex Great biprismated diacosipentacontahexazetton 

98  t_{0,1,2,5}{3,3,3,3,3,3,4} Penticantitruncated 8orthoplex Terigreatorhombated diacosipentacontahexazetton 

99  t_{0,1,3,5}{3,3,3,3,3,3,4} Pentiruncitruncated 8orthoplex Teriprismatotruncated diacosipentacontahexazetton 

100  t_{0,2,3,5}{3,3,3,3,3,3,4} Pentiruncicantellated 8orthoplex Teriprismatorhombated diacosipentacontahexazetton 

101  t_{1,2,3,5}{3,3,3,3,3,3,4} Bistericantitruncated 8orthoplex Bicelligreatorhombated diacosipentacontahexazetton 

102  t_{0,1,4,5}{3,3,3,3,3,3,4} Pentisteritruncated 8orthoplex Tericellitruncated diacosipentacontahexazetton 

103  t_{0,2,4,5}{3,3,3,3,3,3,4} Pentistericantellated 8orthoplex Tericellirhombated diacosipentacontahexazetton 

104  t_{1,2,4,5}{3,3,3,3,3,3,4} Bisteriruncitruncated 8orthoplex Bicelliprismatotruncated diacosipentacontahexazetton 

105  t_{0,3,4,5}{3,3,3,3,3,3,4} Pentisteriruncinated 8orthoplex Tericelliprismated diacosipentacontahexazetton 

106  t_{1,3,4,5}{3,3,3,3,3,3,4} Bisteriruncicantellated 8orthoplex Bicelliprismatorhombated diacosipentacontahexazetton 

107  t_{2,3,4,5}{4,3,3,3,3,3,3} Triruncicantitruncated 8cube Great triprismatoocteractidiacosipentacontahexazetton 

108  t_{0,1,2,6}{3,3,3,3,3,3,4} Hexicantitruncated 8orthoplex Petigreatorhombated diacosipentacontahexazetton 

109  t_{0,1,3,6}{3,3,3,3,3,3,4} Hexiruncitruncated 8orthoplex Petiprismatotruncated diacosipentacontahexazetton 

110  t_{0,2,3,6}{3,3,3,3,3,3,4} Hexiruncicantellated 8orthoplex Petiprismatorhombated diacosipentacontahexazetton 

111  t_{1,2,3,6}{3,3,3,3,3,3,4} Bipenticantitruncated 8orthoplex Biterigreatorhombated diacosipentacontahexazetton 

112  t_{0,1,4,6}{3,3,3,3,3,3,4} Hexisteritruncated 8orthoplex Peticellitruncated diacosipentacontahexazetton 

113  t_{0,2,4,6}{3,3,3,3,3,3,4} Hexistericantellated 8orthoplex Peticellirhombated diacosipentacontahexazetton 

114  t_{1,2,4,6}{3,3,3,3,3,3,4} Bipentiruncitruncated 8orthoplex Biteriprismatotruncated diacosipentacontahexazetton 

115  t_{0,3,4,6}{3,3,3,3,3,3,4} Hexisteriruncinated 8orthoplex Peticelliprismated diacosipentacontahexazetton 

116  t_{1,3,4,6}{4,3,3,3,3,3,3} Bipentiruncicantellated 8cube Biteriprismatorhombiocteractidiacosipentacontahexazetton 

117  t_{1,3,4,5}{4,3,3,3,3,3,3} Bisteriruncicantellated 8cube Bicelliprismatorhombated octeract 

118  t_{0,1,5,6}{3,3,3,3,3,3,4} Hexipentitruncated 8orthoplex Petiteritruncated diacosipentacontahexazetton 

119  t_{0,2,5,6}{3,3,3,3,3,3,4} Hexipenticantellated 8orthoplex Petiterirhombated diacosipentacontahexazetton 

120  t_{1,2,5,6}{4,3,3,3,3,3,3} Bipentisteritruncated 8cube Bitericellitrunkiocteractidiacosipentacontahexazetton 

121  t_{0,3,5,6}{3,3,3,3,3,3,4} Hexipentiruncinated 8orthoplex Petiteriprismated diacosipentacontahexazetton 

122  t_{1,2,4,6}{4,3,3,3,3,3,3} Bipentiruncitruncated 8cube Biteriprismatotruncated octeract 

123  t_{1,2,4,5}{4,3,3,3,3,3,3} Bisteriruncitruncated 8cube Bicelliprismatotruncated octeract 

124  t_{0,4,5,6}{3,3,3,3,3,3,4} Hexipentistericated 8orthoplex Petitericellated diacosipentacontahexazetton 

125  t_{1,2,3,6}{4,3,3,3,3,3,3} Bipenticantitruncated 8cube Biterigreatorhombated octeract 

126  t_{1,2,3,5}{4,3,3,3,3,3,3} Bistericantitruncated 8cube Bicelligreatorhombated octeract 

127  t_{1,2,3,4}{4,3,3,3,3,3,3} Biruncicantitruncated 8cube Great biprismated octeract 

128  t_{0,1,2,7}{3,3,3,3,3,3,4} Hepticantitruncated 8orthoplex Exigreatorhombated diacosipentacontahexazetton 

129  t_{0,1,3,7}{3,3,3,3,3,3,4} Heptiruncitruncated 8orthoplex Exiprismatotruncated diacosipentacontahexazetton 

130  t_{0,2,3,7}{3,3,3,3,3,3,4} Heptiruncicantellated 8orthoplex Exiprismatorhombated diacosipentacontahexazetton 

131  t_{0,4,5,6}{4,3,3,3,3,3,3} Hexipentistericated 8cube Petitericellated octeract 

132  t_{0,1,4,7}{3,3,3,3,3,3,4} Heptisteritruncated 8orthoplex Exicellitruncated diacosipentacontahexazetton 

133  t_{0,2,4,7}{3,3,3,3,3,3,4} Heptistericantellated 8orthoplex Exicellirhombated diacosipentacontahexazetton 

134  t_{0,3,5,6}{4,3,3,3,3,3,3} Hexipentiruncinated 8cube Petiteriprismated octeract 

135  t_{0,3,4,7}{4,3,3,3,3,3,3} Heptisteriruncinated 8cube Exicelliprismatoocteractidiacosipentacontahexazetton 

136  t_{0,3,4,6}{4,3,3,3,3,3,3} Hexisteriruncinated 8cube Peticelliprismated octeract 

137  t_{0,3,4,5}{4,3,3,3,3,3,3} Pentisteriruncinated 8cube Tericelliprismated octeract 

138  t_{0,1,5,7}{3,3,3,3,3,3,4} Heptipentitruncated 8orthoplex Exiteritruncated diacosipentacontahexazetton 

139  t_{0,2,5,7}{4,3,3,3,3,3,3} Heptipenticantellated 8cube Exiterirhombiocteractidiacosipentacontahexazetton 

140  t_{0,2,5,6}{4,3,3,3,3,3,3} Hexipenticantellated 8cube Petiterirhombated octeract 

141  t_{0,2,4,7}{4,3,3,3,3,3,3} Heptistericantellated 8cube Exicellirhombated octeract 

142  t_{0,2,4,6}{4,3,3,3,3,3,3} Hexistericantellated 8cube Peticellirhombated octeract 

143  t_{0,2,4,5}{4,3,3,3,3,3,3} Pentistericantellated 8cube Tericellirhombated octeract 

144  t_{0,2,3,7}{4,3,3,3,3,3,3} Heptiruncicantellated 8cube Exiprismatorhombated octeract 

145  t_{0,2,3,6}{4,3,3,3,3,3,3} Hexiruncicantellated 8cube Petiprismatorhombated octeract 

146  t_{0,2,3,5}{4,3,3,3,3,3,3} Pentiruncicantellated 8cube Teriprismatorhombated octeract 

147  t_{0,2,3,4}{4,3,3,3,3,3,3} Steriruncicantellated 8cube Celliprismatorhombated octeract 

148  t_{0,1,6,7}{4,3,3,3,3,3,3} Heptihexitruncated 8cube Exipetitrunkiocteractidiacosipentacontahexazetton 

149  t_{0,1,5,7}{4,3,3,3,3,3,3} Heptipentitruncated 8cube Exiteritruncated octeract 

150  t_{0,1,5,6}{4,3,3,3,3,3,3} Hexipentitruncated 8cube Petiteritruncated octeract 

151  t_{0,1,4,7}{4,3,3,3,3,3,3} Heptisteritruncated 8cube Exicellitruncated octeract 

152  t_{0,1,4,6}{4,3,3,3,3,3,3} Hexisteritruncated 8cube Peticellitruncated octeract 

153  t_{0,1,4,5}{4,3,3,3,3,3,3} Pentisteritruncated 8cube Tericellitruncated octeract 

154  t_{0,1,3,7}{4,3,3,3,3,3,3} Heptiruncitruncated 8cube Exiprismatotruncated octeract 

155  t_{0,1,3,6}{4,3,3,3,3,3,3} Hexiruncitruncated 8cube Petiprismatotruncated octeract 

156  t_{0,1,3,5}{4,3,3,3,3,3,3} Pentiruncitruncated 8cube Teriprismatotruncated octeract 

157  t_{0,1,3,4}{4,3,3,3,3,3,3} Steriruncitruncated 8cube Celliprismatotruncated octeract 

158  t_{0,1,2,7}{4,3,3,3,3,3,3} Hepticantitruncated 8cube Exigreatorhombated octeract 

159  t_{0,1,2,6}{4,3,3,3,3,3,3} Hexicantitruncated 8cube Petigreatorhombated octeract 

160  t_{0,1,2,5}{4,3,3,3,3,3,3} Penticantitruncated 8cube Terigreatorhombated octeract 

161  t_{0,1,2,4}{4,3,3,3,3,3,3} Stericantitruncated 8cube Celligreatorhombated octeract 

162  t_{0,1,2,3}{4,3,3,3,3,3,3} Runcicantitruncated 8cube Great prismated octeract 

163  t_{0,1,2,3,4}{3,3,3,3,3,3,4} Steriruncicantitruncated 8orthoplex Great cellated diacosipentacontahexazetton 

164  t_{0,1,2,3,5}{3,3,3,3,3,3,4} Pentiruncicantitruncated 8orthoplex Terigreatoprismated diacosipentacontahexazetton 

165  t_{0,1,2,4,5}{3,3,3,3,3,3,4} Pentistericantitruncated 8orthoplex Tericelligreatorhombated diacosipentacontahexazetton 

166  t_{0,1,3,4,5}{3,3,3,3,3,3,4} Pentisteriruncitruncated 8orthoplex Tericelliprismatotruncated diacosipentacontahexazetton 

167  t_{0,2,3,4,5}{3,3,3,3,3,3,4} Pentisteriruncicantellated 8orthoplex Tericelliprismatorhombated diacosipentacontahexazetton 

168  t_{1,2,3,4,5}{3,3,3,3,3,3,4} Bisteriruncicantitruncated 8orthoplex Great bicellated diacosipentacontahexazetton 

169  t_{0,1,2,3,6}{3,3,3,3,3,3,4} Hexiruncicantitruncated 8orthoplex Petigreatoprismated diacosipentacontahexazetton 

170  t_{0,1,2,4,6}{3,3,3,3,3,3,4} Hexistericantitruncated 8orthoplex Peticelligreatorhombated diacosipentacontahexazetton 

171  t_{0,1,3,4,6}{3,3,3,3,3,3,4} Hexisteriruncitruncated 8orthoplex Peticelliprismatotruncated diacosipentacontahexazetton 

172  t_{0,2,3,4,6}{3,3,3,3,3,3,4} Hexisteriruncicantellated 8orthoplex Peticelliprismatorhombated diacosipentacontahexazetton 

173  t_{1,2,3,4,6}{3,3,3,3,3,3,4} Bipentiruncicantitruncated 8orthoplex Biterigreatoprismated diacosipentacontahexazetton 

174  t_{0,1,2,5,6}{3,3,3,3,3,3,4} Hexipenticantitruncated 8orthoplex Petiterigreatorhombated diacosipentacontahexazetton 

175  t_{0,1,3,5,6}{3,3,3,3,3,3,4} Hexipentiruncitruncated 8orthoplex Petiteriprismatotruncated diacosipentacontahexazetton 

176  t_{0,2,3,5,6}{3,3,3,3,3,3,4} Hexipentiruncicantellated 8orthoplex Petiteriprismatorhombated diacosipentacontahexazetton 

177  t_{1,2,3,5,6}{3,3,3,3,3,3,4} Bipentistericantitruncated 8orthoplex Bitericelligreatorhombated diacosipentacontahexazetton 

178  t_{0,1,4,5,6}{3,3,3,3,3,3,4} Hexipentisteritruncated 8orthoplex Petitericellitruncated diacosipentacontahexazetton 

179  t_{0,2,4,5,6}{3,3,3,3,3,3,4} Hexipentistericantellated 8orthoplex Petitericellirhombated diacosipentacontahexazetton 

180  t_{1,2,3,5,6}{4,3,3,3,3,3,3} Bipentistericantitruncated 8cube Bitericelligreatorhombated octeract 

181  t_{0,3,4,5,6}{3,3,3,3,3,3,4} Hexipentisteriruncinated 8orthoplex Petitericelliprismated diacosipentacontahexazetton 

182  t_{1,2,3,4,6}{4,3,3,3,3,3,3} Bipentiruncicantitruncated 8cube Biterigreatoprismated octeract 

183  t_{1,2,3,4,5}{4,3,3,3,3,3,3} Bisteriruncicantitruncated 8cube Great bicellated octeract 

184  t_{0,1,2,3,7}{3,3,3,3,3,3,4} Heptiruncicantitruncated 8orthoplex Exigreatoprismated diacosipentacontahexazetton 

185  t_{0,1,2,4,7}{3,3,3,3,3,3,4} Heptistericantitruncated 8orthoplex Exicelligreatorhombated diacosipentacontahexazetton 

186  t_{0,1,3,4,7}{3,3,3,3,3,3,4} Heptisteriruncitruncated 8orthoplex Exicelliprismatotruncated diacosipentacontahexazetton 

187  t_{0,2,3,4,7}{3,3,3,3,3,3,4} Heptisteriruncicantellated 8orthoplex Exicelliprismatorhombated diacosipentacontahexazetton 

188  t_{0,3,4,5,6}{4,3,3,3,3,3,3} Hexipentisteriruncinated 8cube Petitericelliprismated octeract 

189  t_{0,1,2,5,7}{3,3,3,3,3,3,4} Heptipenticantitruncated 8orthoplex Exiterigreatorhombated diacosipentacontahexazetton 

190  t_{0,1,3,5,7}{3,3,3,3,3,3,4} Heptipentiruncitruncated 8orthoplex Exiteriprismatotruncated diacosipentacontahexazetton 

191  t_{0,2,3,5,7}{3,3,3,3,3,3,4} Heptipentiruncicantellated 8orthoplex Exiteriprismatorhombated diacosipentacontahexazetton 

192  t_{0,2,4,5,6}{4,3,3,3,3,3,3} Hexipentistericantellated 8cube Petitericellirhombated octeract 

193  t_{0,1,4,5,7}{3,3,3,3,3,3,4} Heptipentisteritruncated 8orthoplex Exitericellitruncated diacosipentacontahexazetton 

194  t_{0,2,3,5,7}{4,3,3,3,3,3,3} Heptipentiruncicantellated 8cube Exiteriprismatorhombated octeract 

195  t_{0,2,3,5,6}{4,3,3,3,3,3,3} Hexipentiruncicantellated 8cube Petiteriprismatorhombated octeract 

196  t_{0,2,3,4,7}{4,3,3,3,3,3,3} Heptisteriruncicantellated 8cube Exicelliprismatorhombated octeract 

197  t_{0,2,3,4,6}{4,3,3,3,3,3,3} Hexisteriruncicantellated 8cube Peticelliprismatorhombated octeract 

198  t_{0,2,3,4,5}{4,3,3,3,3,3,3} Pentisteriruncicantellated 8cube Tericelliprismatorhombated octeract 

199  t_{0,1,2,6,7}{3,3,3,3,3,3,4} Heptihexicantitruncated 8orthoplex Exipetigreatorhombated diacosipentacontahexazetton 

200  t_{0,1,3,6,7}{3,3,3,3,3,3,4} Heptihexiruncitruncated 8orthoplex Exipetiprismatotruncated diacosipentacontahexazetton 

201  t_{0,1,4,5,7}{4,3,3,3,3,3,3} Heptipentisteritruncated 8cube Exitericellitruncated octeract 

202  t_{0,1,4,5,6}{4,3,3,3,3,3,3} Hexipentisteritruncated 8cube Petitericellitruncated octeract 

203  t_{0,1,3,6,7}{4,3,3,3,3,3,3} Heptihexiruncitruncated 8cube Exipetiprismatotruncated octeract 

204  t_{0,1,3,5,7}{4,3,3,3,3,3,3} Heptipentiruncitruncated 8cube Exiteriprismatotruncated octeract 

205  t_{0,1,3,5,6}{4,3,3,3,3,3,3} Hexipentiruncitruncated 8cube Petiteriprismatotruncated octeract 

206  t_{0,1,3,4,7}{4,3,3,3,3,3,3} Heptisteriruncitruncated 8cube Exicelliprismatotruncated octeract 

207  t_{0,1,3,4,6}{4,3,3,3,3,3,3} Hexisteriruncitruncated 8cube Peticelliprismatotruncated octeract 

208  t_{0,1,3,4,5}{4,3,3,3,3,3,3} Pentisteriruncitruncated 8cube Tericelliprismatotruncated octeract 

209  t_{0,1,2,6,7}{4,3,3,3,3,3,3} Heptihexicantitruncated 8cube Exipetigreatorhombated octeract 

210  t_{0,1,2,5,7}{4,3,3,3,3,3,3} Heptipenticantitruncated 8cube Exiterigreatorhombated octeract 

211  t_{0,1,2,5,6}{4,3,3,3,3,3,3} Hexipenticantitruncated 8cube Petiterigreatorhombated octeract 

212  t_{0,1,2,4,7}{4,3,3,3,3,3,3} Heptistericantitruncated 8cube Exicelligreatorhombated octeract 

213  t_{0,1,2,4,6}{4,3,3,3,3,3,3} Hexistericantitruncated 8cube Peticelligreatorhombated octeract 

214  t_{0,1,2,4,5}{4,3,3,3,3,3,3} Pentistericantitruncated 8cube Tericelligreatorhombated octeract 

215  t_{0,1,2,3,7}{4,3,3,3,3,3,3} Heptiruncicantitruncated 8cube Exigreatoprismated octeract 

216  t_{0,1,2,3,6}{4,3,3,3,3,3,3} Hexiruncicantitruncated 8cube Petigreatoprismated octeract 

217  t_{0,1,2,3,5}{4,3,3,3,3,3,3} Pentiruncicantitruncated 8cube Terigreatoprismated octeract 

218  t_{0,1,2,3,4}{4,3,3,3,3,3,3} Steriruncicantitruncated 8cube Great cellated octeract 

219  t_{0,1,2,3,4,5}{3,3,3,3,3,3,4} Pentisteriruncicantitruncated 8orthoplex Great terated diacosipentacontahexazetton 

220  t_{0,1,2,3,4,6}{3,3,3,3,3,3,4} Hexisteriruncicantitruncated 8orthoplex Petigreatocellated diacosipentacontahexazetton 

221  t_{0,1,2,3,5,6}{3,3,3,3,3,3,4} Hexipentiruncicantitruncated 8orthoplex Petiterigreatoprismated diacosipentacontahexazetton 

222  t_{0,1,2,4,5,6}{3,3,3,3,3,3,4} Hexipentistericantitruncated 8orthoplex Petitericelligreatorhombated diacosipentacontahexazetton 

223  t_{0,1,3,4,5,6}{3,3,3,3,3,3,4} Hexipentisteriruncitruncated 8orthoplex Petitericelliprismatotruncated diacosipentacontahexazetton 

224  t_{0,2,3,4,5,6}{3,3,3,3,3,3,4} Hexipentisteriruncicantellated 8orthoplex Petitericelliprismatorhombated diacosipentacontahexazetton 

225  t_{1,2,3,4,5,6}{4,3,3,3,3,3,3} Bipentisteriruncicantitruncated 8cube Great biteriocteractidiacosipentacontahexazetton 

226  t_{0,1,2,3,4,7}{3,3,3,3,3,3,4} Heptisteriruncicantitruncated 8orthoplex Exigreatocellated diacosipentacontahexazetton 

227  t_{0,1,2,3,5,7}{3,3,3,3,3,3,4} Heptipentiruncicantitruncated 8orthoplex Exiterigreatoprismated diacosipentacontahexazetton 

228  t_{0,1,2,4,5,7}{3,3,3,3,3,3,4} Heptipentistericantitruncated 8orthoplex Exitericelligreatorhombated diacosipentacontahexazetton 

229  t_{0,1,3,4,5,7}{3,3,3,3,3,3,4} Heptipentisteriruncitruncated 8orthoplex Exitericelliprismatotruncated diacosipentacontahexazetton 

230  t_{0,2,3,4,5,7}{4,3,3,3,3,3,3} Heptipentisteriruncicantellated 8cube Exitericelliprismatorhombiocteractidiacosipentacontahexazetton 

231  t_{0,2,3,4,5,6}{4,3,3,3,3,3,3} Hexipentisteriruncicantellated 8cube Petitericelliprismatorhombated octeract 

232  t_{0,1,2,3,6,7}{3,3,3,3,3,3,4} Heptihexiruncicantitruncated 8orthoplex Exipetigreatoprismated diacosipentacontahexazetton 

233  t_{0,1,2,4,6,7}{3,3,3,3,3,3,4} Heptihexistericantitruncated 8orthoplex Exipeticelligreatorhombated diacosipentacontahexazetton 

234  t_{0,1,3,4,6,7}{4,3,3,3,3,3,3} Heptihexisteriruncitruncated 8cube Exipeticelliprismatotrunkiocteractidiacosipentacontahexazetton 

235  t_{0,1,3,4,5,7}{4,3,3,3,3,3,3} Heptipentisteriruncitruncated 8cube Exitericelliprismatotruncated octeract 

236  t_{0,1,3,4,5,6}{4,3,3,3,3,3,3} Hexipentisteriruncitruncated 8cube Petitericelliprismatotruncated octeract 

237  t_{0,1,2,5,6,7}{4,3,3,3,3,3,3} Heptihexipenticantitruncated 8cube Exipetiterigreatorhombiocteractidiacosipentacontahexazetton 

238  t_{0,1,2,4,6,7}{4,3,3,3,3,3,3} Heptihexistericantitruncated 8cube Exipeticelligreatorhombated octeract 

239  t_{0,1,2,4,5,7}{4,3,3,3,3,3,3} Heptipentistericantitruncated 8cube Exitericelligreatorhombated octeract 

240  t_{0,1,2,4,5,6}{4,3,3,3,3,3,3} Hexipentistericantitruncated 8cube Petitericelligreatorhombated octeract 

241  t_{0,1,2,3,6,7}{4,3,3,3,3,3,3} Heptihexiruncicantitruncated 8cube Exipetigreatoprismated octeract 

242  t_{0,1,2,3,5,7}{4,3,3,3,3,3,3} Heptipentiruncicantitruncated 8cube Exiterigreatoprismated octeract 

243  t_{0,1,2,3,5,6}{4,3,3,3,3,3,3} Hexipentiruncicantitruncated 8cube Petiterigreatoprismated octeract 

244  t_{0,1,2,3,4,7}{4,3,3,3,3,3,3} Heptisteriruncicantitruncated 8cube Exigreatocellated octeract 

245  t_{0,1,2,3,4,6}{4,3,3,3,3,3,3} Hexisteriruncicantitruncated 8cube Petigreatocellated octeract 

246  t_{0,1,2,3,4,5}{4,3,3,3,3,3,3} Pentisteriruncicantitruncated 8cube Great terated octeract 

247  t_{0,1,2,3,4,5,6}{3,3,3,3,3,3,4} Hexipentisteriruncicantitruncated 8orthoplex Great petated diacosipentacontahexazetton 

248  t_{0,1,2,3,4,5,7}{3,3,3,3,3,3,4} Heptipentisteriruncicantitruncated 8orthoplex Exigreatoterated diacosipentacontahexazetton 

249  t_{0,1,2,3,4,6,7}{3,3,3,3,3,3,4} Heptihexisteriruncicantitruncated 8orthoplex Exipetigreatocellated diacosipentacontahexazetton 

250  t_{0,1,2,3,5,6,7}{3,3,3,3,3,3,4} Heptihexipentiruncicantitruncated 8orthoplex Exipetiterigreatoprismated diacosipentacontahexazetton 

251  t_{0,1,2,3,5,6,7}{4,3,3,3,3,3,3} Heptihexipentiruncicantitruncated 8cube Exipetiterigreatoprismated octeract 

252  t_{0,1,2,3,4,6,7}{4,3,3,3,3,3,3} Heptihexisteriruncicantitruncated 8cube Exipetigreatocellated octeract 

253  t_{0,1,2,3,4,5,7}{4,3,3,3,3,3,3} Heptipentisteriruncicantitruncated 8cube Exigreatoterated octeract 

254  t_{0,1,2,3,4,5,6}{4,3,3,3,3,3,3} Hexipentisteriruncicantitruncated 8cube Great petated octeract 

255  t_{0,1,2,3,4,5,6,7}{4,3,3,3,3,3,3} Omnitruncated 8cube Great exiocteractidiacosipentacontahexazetton 

256  h_{0}{4,3,3,3,3,3,3} 8demicube Hemiocteract 
References
Klitzing, Richard. "8D uniform polytopes (polyzetta)".
Notes
Fundamental convex regular and uniform polytopes in dimensions 2–10



Family  A_{n}  B_{n}  I_{2}(p) / D_{n}  E_{6} / E_{7} / E_{8} / F_{4} / G_{2}  H_{n}  
Regular polygon  Triangle  Square  pgon  Hexagon  Pentagon  
Uniform polyhedron  Tetrahedron  Octahedron • Cube  Demicube  Dodecahedron • Icosahedron  
Uniform 4polytope  5cell  16cell • Tesseract  Demitesseract  24cell  120cell • 600cell  
Uniform 5polytope  5simplex  5orthoplex • 5cube  5demicube  
Uniform 6polytope  6simplex  6orthoplex • 6cube  6demicube  1_{22} • 2_{21}  
Uniform 7polytope  7simplex  7orthoplex • 7cube  7demicube  1_{32} • 2_{31} • 3_{21}  
Uniform 8polytope  8simplex  8orthoplex • 8cube  8demicube  1_{42} • 2_{41} • 4_{21}  
Uniform 9polytope  9simplex  9orthoplex • 9cube  9demicube  
Uniform 10polytope  10simplex  10orthoplex • 10cube  10demicube  
Uniform npolytope  nsimplex  northoplex • ncube  ndemicube  1_{k2} • 2_{k1} • k_{21}  npentagonal polytope  
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds 
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World  Scientific Library
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