Polytope of Type {2,8}

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

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(1,2);
s1 := Sym(10)!(4,5)(6,7)(8,9);
s2 := Sym(10)!( 3, 4)( 5, 6)( 7, 8)( 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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope