Polytope of Type {8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1280h
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 32, 320, 80
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {8,10}*640d, {4,20}*640e
   4-fold quotients : {8,5}*320b, {4,10}*320b
   8-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 94)(  2, 93)(  3, 96)(  4, 95)(  5, 90)(  6, 89)(  7, 92)(  8, 91)
(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 53)( 18, 54)( 19, 55)( 20, 56)
( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25,102)( 26,101)( 27,104)( 28,103)
( 29, 98)( 30, 97)( 31,100)( 32, 99)( 33,126)( 34,125)( 35,128)( 36,127)
( 37,122)( 38,121)( 39,124)( 40,123)( 41, 47)( 42, 48)( 43, 45)( 44, 46)
( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)( 64, 65)
( 73,110)( 74,109)( 75,112)( 76,111)( 77,106)( 78,105)( 79,108)( 80,107)
( 81, 88)( 82, 87)( 83, 86)( 84, 85)(113,118)(114,117)(115,120)(116,119);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
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*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*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, 94)(  2, 93)(  3, 96)(  4, 95)(  5, 90)(  6, 89)(  7, 92)
(  8, 91)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 53)( 18, 54)( 19, 55)
( 20, 56)( 21, 49)( 22, 50)( 23, 51)( 24, 52)( 25,102)( 26,101)( 27,104)
( 28,103)( 29, 98)( 30, 97)( 31,100)( 32, 99)( 33,126)( 34,125)( 35,128)
( 36,127)( 37,122)( 38,121)( 39,124)( 40,123)( 41, 47)( 42, 48)( 43, 45)
( 44, 46)( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)
( 64, 65)( 73,110)( 74,109)( 75,112)( 76,111)( 77,106)( 78,105)( 79,108)
( 80,107)( 81, 88)( 82, 87)( 83, 86)( 84, 85)(113,118)(114,117)(115,120)
(116,119);
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
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*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
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