Polytope of Type {10,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*1280c
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 80, 320, 64
Order of s0s1s2 : 10
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,8}*640a, {10,8}*640a, {10,8}*640b, {10,8}*640c, {10,8}*640d, {10,4}*640b
   4-fold quotients : {5,8}*320a, {5,8}*320b, {5,4}*320, {10,4}*320a, {10,4}*320b
   8-fold quotients : {5,4}*160
   32-fold quotients : {10,2}*40
   64-fold quotients : {5,2}*20
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 2.
      32 facets:
         32 of {10}*20
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      32 facets:
         32 of {10}*20
      40 vertex figures:
         40 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 4.
      16 facets:
         16 of {10}*20
      20 vertex figures:
         20 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 4.
      16 facets:
         16 of {10}*20
      20 vertex figures:
         20 of {8}*16

Permutation Representation (GAP) : 
s0 := ( 17, 26)( 18, 25)( 19, 28)( 20, 27)( 21, 30)( 22, 29)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112);;
s1 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9,102)( 10,101)( 11,104)( 12,103)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17, 62)( 18, 61)( 19, 64)( 20, 63)( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 78)( 34, 77)( 35, 80)( 36, 79)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 41, 46)( 42, 45)( 43, 48)( 44, 47)( 49,117)( 50,118)( 51,119)( 52,120)( 53,113)( 54,114)( 55,115)( 56,116)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 81,126)( 82,125)( 83,128)( 84,127)( 85,122)( 86,121)( 87,124)( 88,123)(105,110)(106,109)(107,112)(108,111);;
s2 := (  1, 12)(  2, 11)(  3, 10)(  4,  9)(  5, 16)(  6, 15)(  7, 14)(  8, 13)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 44)( 34, 43)( 35, 42)( 36, 41)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 65, 76)( 66, 75)( 67, 74)( 68, 73)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 97,108)( 98,107)( 99,106)(100,105)(101,112)(102,111)(103,110)(104,109)(113,124)(114,123)(115,122)(116,121)(117,128)(118,127)(119,126)(120,125);;
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(128)!( 17, 26)( 18, 25)( 19, 28)( 20, 27)( 21, 30)( 22, 29)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112);
s1 := Sym(128)!(  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9,102)( 10,101)( 11,104)( 12,103)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17, 62)( 18, 61)( 19, 64)( 20, 63)( 21, 58)( 22, 57)( 23, 60)( 24, 59)( 25, 94)( 26, 93)( 27, 96)( 28, 95)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 78)( 34, 77)( 35, 80)( 36, 79)( 37, 74)( 38, 73)( 39, 76)( 40, 75)( 41, 46)( 42, 45)( 43, 48)( 44, 47)( 49,117)( 50,118)( 51,119)( 52,120)( 53,113)( 54,114)( 55,115)( 56,116)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 81,126)( 82,125)( 83,128)( 84,127)( 85,122)( 86,121)( 87,124)( 88,123)(105,110)(106,109)(107,112)(108,111);
s2 := Sym(128)!(  1, 12)(  2, 11)(  3, 10)(  4,  9)(  5, 16)(  6, 15)(  7, 14)(  8, 13)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 44)( 34, 43)( 35, 42)( 36, 41)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 65, 76)( 66, 75)( 67, 74)( 68, 73)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 97,108)( 98,107)( 99,106)(100,105)(101,112)(102,111)(103,110)(104,109)(113,124)(114,123)(115,122)(116,121)(117,128)(118,127)(119,126)(120,125);
poly := sub<Sym(128)|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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle