Polytope of Type {8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2}*32
if this polytope has a name.
Group : SmallGroup(32,39)
Rank : 3
Schlafli Type : {8,2}
Number of vertices, edges, etc : 8, 8, 2
Order of s0s1s2 : 8
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{8,2,2} of size 64
{8,2,3} of size 96
{8,2,4} of size 128
{8,2,5} of size 160
{8,2,6} of size 192
{8,2,7} of size 224
{8,2,8} of size 256
{8,2,9} of size 288
{8,2,10} of size 320
{8,2,11} of size 352
{8,2,12} of size 384
{8,2,13} of size 416
{8,2,14} of size 448
{8,2,15} of size 480
{8,2,17} of size 544
{8,2,18} of size 576
{8,2,19} of size 608
{8,2,20} of size 640
{8,2,21} of size 672
{8,2,22} of size 704
{8,2,23} of size 736
{8,2,24} of size 768
{8,2,25} of size 800
{8,2,26} of size 832
{8,2,27} of size 864
{8,2,28} of size 896
{8,2,29} of size 928
{8,2,30} of size 960
{8,2,31} of size 992
{8,2,33} of size 1056
{8,2,34} of size 1088
{8,2,35} of size 1120
{8,2,36} of size 1152
{8,2,37} of size 1184
{8,2,38} of size 1216
{8,2,39} of size 1248
{8,2,40} of size 1280
{8,2,41} of size 1312
{8,2,42} of size 1344
{8,2,43} of size 1376
{8,2,44} of size 1408
{8,2,45} of size 1440
{8,2,46} of size 1472
{8,2,47} of size 1504
{8,2,49} of size 1568
{8,2,50} of size 1600
{8,2,51} of size 1632
{8,2,52} of size 1664
{8,2,53} of size 1696
{8,2,54} of size 1728
{8,2,55} of size 1760
{8,2,56} of size 1792
{8,2,57} of size 1824
{8,2,58} of size 1856
{8,2,59} of size 1888
{8,2,60} of size 1920
{8,2,61} of size 1952
{8,2,62} of size 1984
Vertex Figure Of :
{2,8,2} of size 64
{4,8,2} of size 128
{4,8,2} of size 128
{6,8,2} of size 192
{3,8,2} of size 192
{4,8,2} of size 256
{8,8,2} of size 256
{8,8,2} of size 256
{8,8,2} of size 256
{8,8,2} of size 256
{4,8,2} of size 256
{10,8,2} of size 320
{12,8,2} of size 384
{12,8,2} of size 384
{3,8,2} of size 384
{6,8,2} of size 384
{6,8,2} of size 384
{6,8,2} of size 384
{14,8,2} of size 448
{8,8,2} of size 512
{4,8,2} of size 512
{8,8,2} of size 512
{8,8,2} of size 512
{8,8,2} of size 512
{16,8,2} of size 512
{16,8,2} of size 512
{16,8,2} of size 512
{16,8,2} of size 512
{16,8,2} of size 512
{16,8,2} of size 512
{4,8,2} of size 512
{4,8,2} of size 512
{4,8,2} of size 512
{8,8,2} of size 512
{8,8,2} of size 512
{8,8,2} of size 512
{8,8,2} of size 512
{18,8,2} of size 576
{9,8,2} of size 576
{6,8,2} of size 576
{20,8,2} of size 640
{20,8,2} of size 640
{5,8,2} of size 640
{5,8,2} of size 640
{3,8,2} of size 672
{3,8,2} of size 672
{4,8,2} of size 672
{4,8,2} of size 672
{6,8,2} of size 672
{6,8,2} of size 672
{7,8,2} of size 672
{7,8,2} of size 672
{8,8,2} of size 672
{8,8,2} of size 672
{22,8,2} of size 704
{12,8,2} of size 768
{24,8,2} of size 768
{24,8,2} of size 768
{24,8,2} of size 768
{24,8,2} of size 768
{12,8,2} of size 768
{3,8,2} of size 768
{6,8,2} of size 768
{12,8,2} of size 768
{12,8,2} of size 768
{6,8,2} of size 768
{6,8,2} of size 768
{6,8,2} of size 768
{6,8,2} of size 768
{12,8,2} of size 768
{12,8,2} of size 768
{6,8,2} of size 768
{12,8,2} of size 768
{12,8,2} of size 768
{6,8,2} of size 768
{26,8,2} of size 832
{28,8,2} of size 896
{28,8,2} of size 896
{30,8,2} of size 960
{5,8,2} of size 960
{6,8,2} of size 960
{6,8,2} of size 960
{15,8,2} of size 960
{34,8,2} of size 1088
{36,8,2} of size 1152
{4,8,2} of size 1152
{12,8,2} of size 1152
{36,8,2} of size 1152
{4,8,2} of size 1152
{12,8,2} of size 1152
{9,8,2} of size 1152
{18,8,2} of size 1152
{18,8,2} of size 1152
{18,8,2} of size 1152
{38,8,2} of size 1216
{20,8,2} of size 1280
{40,8,2} of size 1280
{40,8,2} of size 1280
{40,8,2} of size 1280
{40,8,2} of size 1280
{20,8,2} of size 1280
{5,8,2} of size 1280
{10,8,2} of size 1280
{10,8,2} of size 1280
{10,8,2} of size 1280
{10,8,2} of size 1280
{5,8,2} of size 1280
{42,8,2} of size 1344
{21,8,2} of size 1344
{3,8,2} of size 1344
{3,8,2} of size 1344
{4,8,2} of size 1344
{4,8,2} of size 1344
{4,8,2} of size 1344
{4,8,2} of size 1344
{4,8,2} of size 1344
{4,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{6,8,2} of size 1344
{7,8,2} of size 1344
{7,8,2} of size 1344
{8,8,2} of size 1344
{8,8,2} of size 1344
{8,8,2} of size 1344
{8,8,2} of size 1344
{8,8,2} of size 1344
{8,8,2} of size 1344
{14,8,2} of size 1344
{14,8,2} of size 1344
{14,8,2} of size 1344
{14,8,2} of size 1344
{44,8,2} of size 1408
{44,8,2} of size 1408
{3,8,2} of size 1440
{4,8,2} of size 1440
{5,8,2} of size 1440
{5,8,2} of size 1440
{8,8,2} of size 1440
{10,8,2} of size 1440
{10,8,2} of size 1440
{46,8,2} of size 1472
{8,8,2} of size 1568
{8,8,2} of size 1568
{14,8,2} of size 1568
{14,8,2} of size 1568
{50,8,2} of size 1600
{10,8,2} of size 1600
{52,8,2} of size 1664
{52,8,2} of size 1664
{54,8,2} of size 1728
{27,8,2} of size 1728
{6,8,2} of size 1728
{6,8,2} of size 1728
{28,8,2} of size 1792
{56,8,2} of size 1792
{56,8,2} of size 1792
{56,8,2} of size 1792
{56,8,2} of size 1792
{28,8,2} of size 1792
{58,8,2} of size 1856
{60,8,2} of size 1920
{60,8,2} of size 1920
{15,8,2} of size 1920
{30,8,2} of size 1920
{15,8,2} of size 1920
{15,8,2} of size 1920
{30,8,2} of size 1920
{30,8,2} of size 1920
{10,8,2} of size 1920
{10,8,2} of size 1920
{6,8,2} of size 1920
{10,8,2} of size 1920
{10,8,2} of size 1920
{6,8,2} of size 1920
{62,8,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2}*16
4-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,4}*64a, {16,2}*64
3-fold covers : {24,2}*96, {8,6}*96
4-fold covers : {8,4}*128a, {8,8}*128b, {8,8}*128c, {16,4}*128a, {16,4}*128b, {32,2}*128
5-fold covers : {40,2}*160, {8,10}*160
6-fold covers : {24,4}*192a, {8,12}*192a, {48,2}*192, {16,6}*192
7-fold covers : {56,2}*224, {8,14}*224
8-fold covers : {8,8}*256a, {8,4}*256a, {8,8}*256d, {16,4}*256a, {16,4}*256b, {8,16}*256a, {8,16}*256b, {8,16}*256d, {16,8}*256c, {16,8}*256d, {8,16}*256f, {16,8}*256e, {16,8}*256f, {32,4}*256a, {32,4}*256b, {64,2}*256
9-fold covers : {72,2}*288, {8,18}*288, {24,6}*288a, {24,6}*288b, {24,6}*288c, {8,6}*288
10-fold covers : {40,4}*320a, {8,20}*320a, {80,2}*320, {16,10}*320
11-fold covers : {88,2}*352, {8,22}*352
12-fold covers : {24,4}*384a, {8,24}*384b, {24,8}*384a, {24,8}*384b, {8,12}*384a, {8,24}*384d, {48,4}*384a, {48,4}*384b, {16,12}*384a, {16,12}*384b, {96,2}*384, {32,6}*384, {24,4}*384c, {8,6}*384g, {24,6}*384a
13-fold covers : {104,2}*416, {8,26}*416
14-fold covers : {56,4}*448a, {8,28}*448a, {112,2}*448, {16,14}*448
15-fold covers : {24,10}*480, {40,6}*480, {120,2}*480, {8,30}*480
16-fold covers : {16,4}*512a, {16,8}*512a, {16,8}*512b, {16,16}*512b, {16,16}*512c, {16,16}*512e, {16,16}*512f, {16,16}*512h, {16,16}*512i, {16,16}*512j, {16,16}*512k, {8,16}*512c, {16,8}*512c, {8,16}*512d, {16,8}*512d, {8,16}*512e, {16,8}*512e, {8,16}*512f, {16,8}*512f, {8,8}*512a, {8,8}*512b, {8,8}*512c, {8,4}*512a, {8,8}*512f, {16,4}*512b, {8,4}*512b, {8,4}*512c, {8,8}*512l, {8,8}*512n, {16,4}*512c, {16,4}*512d, {8,8}*512q, {8,8}*512s, {16,8}*512g, {16,8}*512h, {32,4}*512a, {32,4}*512b, {8,32}*512b, {32,8}*512a, {32,8}*512b, {8,32}*512d, {32,8}*512c, {32,8}*512d, {64,4}*512a, {64,4}*512b, {128,2}*512
17-fold covers : {136,2}*544, {8,34}*544
18-fold covers : {72,4}*576a, {8,36}*576a, {144,2}*576, {16,18}*576, {48,6}*576a, {48,6}*576b, {24,12}*576b, {24,12}*576c, {24,12}*576d, {48,6}*576c, {16,6}*576, {8,12}*576a, {8,4}*576a, {24,4}*576a
19-fold covers : {152,2}*608, {8,38}*608
20-fold covers : {40,4}*640a, {8,40}*640b, {40,8}*640a, {40,8}*640b, {8,20}*640a, {8,40}*640d, {80,4}*640a, {80,4}*640b, {16,20}*640a, {16,20}*640b, {160,2}*640, {32,10}*640
21-fold covers : {24,14}*672, {56,6}*672, {168,2}*672, {8,42}*672
22-fold covers : {88,4}*704a, {8,44}*704a, {176,2}*704, {16,22}*704
23-fold covers : {184,2}*736, {8,46}*736
24-fold covers : {8,24}*768a, {24,8}*768a, {8,12}*768a, {24,4}*768a, {8,24}*768c, {24,8}*768d, {16,12}*768a, {48,4}*768a, {16,12}*768b, {48,4}*768b, {8,48}*768a, {24,16}*768a, {8,48}*768b, {24,16}*768b, {16,24}*768c, {8,48}*768d, {48,8}*768c, {48,8}*768d, {16,24}*768d, {24,16}*768d, {16,24}*768e, {8,48}*768f, {48,8}*768e, {48,8}*768f, {16,24}*768f, {24,16}*768f, {32,12}*768a, {96,4}*768a, {32,12}*768b, {96,4}*768b, {64,6}*768, {192,2}*768, {24,8}*768i, {24,8}*768k, {8,6}*768j, {24,6}*768, {8,12}*768o, {24,12}*768a, {24,4}*768i, {8,12}*768u, {24,12}*768c, {48,4}*768c, {48,4}*768d, {16,6}*768b, {48,6}*768a, {16,6}*768c, {48,6}*768b
25-fold covers : {200,2}*800, {8,50}*800, {40,10}*800a, {40,10}*800b, {40,10}*800c, {8,10}*800
26-fold covers : {104,4}*832a, {8,52}*832a, {208,2}*832, {16,26}*832
27-fold covers : {216,2}*864, {8,54}*864, {72,6}*864a, {72,6}*864b, {24,18}*864a, {24,6}*864a, {24,6}*864b, {24,18}*864b, {24,6}*864c, {8,6}*864a, {24,6}*864d, {24,6}*864e, {24,6}*864f, {8,6}*864b, {24,6}*864g, {24,6}*864h
28-fold covers : {56,4}*896a, {8,56}*896b, {56,8}*896a, {56,8}*896b, {8,28}*896a, {8,56}*896d, {112,4}*896a, {112,4}*896b, {16,28}*896a, {16,28}*896b, {224,2}*896, {32,14}*896
29-fold covers : {232,2}*928, {8,58}*928
30-fold covers : {48,10}*960, {80,6}*960, {24,20}*960a, {40,12}*960a, {120,4}*960a, {8,60}*960a, {240,2}*960, {16,30}*960
31-fold covers : {248,2}*992, {8,62}*992
33-fold covers : {24,22}*1056, {88,6}*1056, {264,2}*1056, {8,66}*1056
34-fold covers : {8,68}*1088a, {136,4}*1088a, {16,34}*1088, {272,2}*1088
35-fold covers : {40,14}*1120, {56,10}*1120, {280,2}*1120, {8,70}*1120
36-fold covers : {8,36}*1152a, {72,4}*1152a, {24,12}*1152a, {24,12}*1152b, {24,12}*1152c, {8,4}*1152a, {24,4}*1152a, {8,12}*1152a, {8,72}*1152a, {8,72}*1152c, {72,8}*1152b, {72,8}*1152c, {24,24}*1152b, {24,24}*1152c, {24,24}*1152e, {24,24}*1152f, {24,24}*1152g, {24,24}*1152h, {8,8}*1152a, {24,8}*1152a, {8,8}*1152b, {8,24}*1152b, {8,24}*1152c, {24,8}*1152c, {16,36}*1152a, {144,4}*1152a, {48,12}*1152a, {48,12}*1152b, {48,12}*1152c, {16,4}*1152a, {48,4}*1152a, {16,12}*1152a, {16,36}*1152b, {144,4}*1152b, {48,12}*1152d, {48,12}*1152e, {48,12}*1152f, {16,4}*1152b, {48,4}*1152b, {16,12}*1152b, {32,18}*1152, {288,2}*1152, {96,6}*1152a, {96,6}*1152b, {96,6}*1152c, {32,6}*1152, {72,4}*1152c, {8,18}*1152g, {24,12}*1152o, {24,12}*1152p, {24,6}*1152g, {24,6}*1152h, {24,6}*1152j, {24,6}*1152k
37-fold covers : {8,74}*1184, {296,2}*1184
38-fold covers : {8,76}*1216a, {152,4}*1216a, {16,38}*1216, {304,2}*1216
39-fold covers : {24,26}*1248, {104,6}*1248, {312,2}*1248, {8,78}*1248
40-fold covers : {8,40}*1280a, {40,8}*1280a, {8,20}*1280a, {40,4}*1280a, {8,40}*1280c, {40,8}*1280d, {16,20}*1280a, {80,4}*1280a, {16,20}*1280b, {80,4}*1280b, {8,80}*1280a, {40,16}*1280a, {8,80}*1280b, {40,16}*1280b, {16,40}*1280c, {8,80}*1280d, {80,8}*1280c, {80,8}*1280d, {16,40}*1280d, {40,16}*1280d, {16,40}*1280e, {8,80}*1280f, {80,8}*1280e, {80,8}*1280f, {16,40}*1280f, {40,16}*1280f, {32,20}*1280a, {160,4}*1280a, {32,20}*1280b, {160,4}*1280b, {64,10}*1280, {320,2}*1280
41-fold covers : {8,82}*1312, {328,2}*1312
42-fold covers : {48,14}*1344, {112,6}*1344, {24,28}*1344a, {56,12}*1344a, {168,4}*1344a, {8,84}*1344a, {336,2}*1344, {16,42}*1344
43-fold covers : {8,86}*1376, {344,2}*1376
44-fold covers : {8,44}*1408a, {88,4}*1408a, {8,88}*1408a, {8,88}*1408c, {88,8}*1408b, {88,8}*1408c, {16,44}*1408a, {176,4}*1408a, {16,44}*1408b, {176,4}*1408b, {32,22}*1408, {352,2}*1408
45-fold covers : {72,10}*1440, {40,18}*1440, {360,2}*1440, {8,90}*1440, {120,6}*1440a, {24,30}*1440a, {24,30}*1440b, {120,6}*1440b, {120,6}*1440c, {24,30}*1440c, {8,30}*1440, {40,6}*1440
46-fold covers : {8,92}*1472a, {184,4}*1472a, {16,46}*1472, {368,2}*1472
47-fold covers : {8,94}*1504, {376,2}*1504
49-fold covers : {392,2}*1568, {8,98}*1568, {56,14}*1568a, {56,14}*1568b, {56,14}*1568c, {8,14}*1568a, {8,14}*1568b, {8,14}*1568c
50-fold covers : {200,4}*1600a, {8,100}*1600a, {400,2}*1600, {16,50}*1600, {80,10}*1600a, {80,10}*1600b, {40,20}*1600b, {40,20}*1600c, {40,20}*1600d, {80,10}*1600c, {16,10}*1600, {8,20}*1600a, {8,4}*1600a, {40,4}*1600a
51-fold covers : {24,34}*1632, {136,6}*1632, {408,2}*1632, {8,102}*1632
52-fold covers : {8,52}*1664a, {104,4}*1664a, {8,104}*1664a, {8,104}*1664c, {104,8}*1664b, {104,8}*1664c, {16,52}*1664a, {208,4}*1664a, {16,52}*1664b, {208,4}*1664b, {32,26}*1664, {416,2}*1664
53-fold covers : {8,106}*1696, {424,2}*1696
54-fold covers : {216,4}*1728a, {8,108}*1728a, {432,2}*1728, {16,54}*1728, {144,6}*1728a, {144,6}*1728b, {48,18}*1728a, {48,6}*1728a, {48,6}*1728b, {24,36}*1728b, {24,12}*1728b, {72,12}*1728a, {72,12}*1728b, {24,36}*1728c, {24,12}*1728c, {24,12}*1728d, {48,18}*1728b, {48,6}*1728c, {16,6}*1728a, {48,6}*1728d, {48,6}*1728e, {8,12}*1728a, {24,12}*1728g, {24,12}*1728h, {8,12}*1728b, {24,4}*1728a, {24,4}*1728b, {24,12}*1728i, {24,12}*1728j, {48,6}*1728f, {24,12}*1728o, {24,4}*1728e, {24,4}*1728f, {8,12}*1728e, {24,12}*1728q, {16,6}*1728b, {48,6}*1728g, {8,12}*1728g, {24,12}*1728s, {48,6}*1728h, {24,12}*1728u, {24,12}*1728v
55-fold covers : {40,22}*1760, {88,10}*1760, {440,2}*1760, {8,110}*1760
56-fold covers : {8,56}*1792a, {56,8}*1792a, {8,28}*1792a, {56,4}*1792a, {8,56}*1792c, {56,8}*1792d, {16,28}*1792a, {112,4}*1792a, {16,28}*1792b, {112,4}*1792b, {8,112}*1792a, {56,16}*1792a, {8,112}*1792b, {56,16}*1792b, {16,56}*1792c, {8,112}*1792d, {112,8}*1792c, {112,8}*1792d, {16,56}*1792d, {56,16}*1792d, {16,56}*1792e, {8,112}*1792f, {112,8}*1792e, {112,8}*1792f, {16,56}*1792f, {56,16}*1792f, {32,28}*1792a, {224,4}*1792a, {32,28}*1792b, {224,4}*1792b, {64,14}*1792, {448,2}*1792
57-fold covers : {24,38}*1824, {152,6}*1824, {456,2}*1824, {8,114}*1824
58-fold covers : {8,116}*1856a, {232,4}*1856a, {16,58}*1856, {464,2}*1856
59-fold covers : {8,118}*1888, {472,2}*1888
60-fold covers : {8,60}*1920a, {120,4}*1920a, {40,12}*1920a, {24,20}*1920a, {8,120}*1920a, {8,120}*1920c, {120,8}*1920b, {120,8}*1920c, {24,40}*1920a, {40,24}*1920a, {24,40}*1920b, {40,24}*1920c, {16,60}*1920a, {240,4}*1920a, {80,12}*1920a, {48,20}*1920a, {16,60}*1920b, {240,4}*1920b, {80,12}*1920b, {48,20}*1920b, {32,30}*1920, {480,2}*1920, {96,10}*1920, {160,6}*1920, {24,20}*1920c, {40,6}*1920d, {120,6}*1920a, {24,30}*1920a, {120,4}*1920c, {8,30}*1920g, {8,10}*1920a, {24,6}*1920a, {24,10}*1920c, {8,6}*1920a, {24,4}*1920a, {40,4}*1920a, {40,6}*1920e, {24,10}*1920d, {40,6}*1920f, {40,10}*1920a
61-fold covers : {8,122}*1952, {488,2}*1952
62-fold covers : {8,124}*1984a, {248,4}*1984a, {16,62}*1984, {496,2}*1984
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(10)!(2,3)(4,5)(6,7);
s1 := Sym(10)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(10)!( 9,10);
poly := sub<Sym(10)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope