Polytope of Type {8,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,10}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {8,10}
Number of vertices, edges, etc : 64, 320, 80
Order of s0s1s2 : 20
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,10}*640a, {8,5}*640b
   4-fold quotients : {4,5}*320
   8-fold quotients : {4,5}*160
   64-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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