Polytope of Type {8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1280l
if this polytope has a name.
Group : SmallGroup(1280,1116427)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 32, 320, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,20}*640c, {8,10}*640b
   4-fold quotients : {8,5}*320b, {4,10}*320a
   8-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,123)(  2,124)(  3,121)(  4,122)(  5,127)(  6,128)(  7,125)(  8,126)
(  9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)( 16,117)
( 17,108)( 18,107)( 19,106)( 20,105)( 21,112)( 22,111)( 23,110)( 24,109)
( 25, 99)( 26,100)( 27, 97)( 28, 98)( 29,103)( 30,104)( 31,101)( 32,102)
( 33, 91)( 34, 92)( 35, 89)( 36, 90)( 37, 95)( 38, 96)( 39, 93)( 40, 94)
( 41, 84)( 42, 83)( 43, 82)( 44, 81)( 45, 88)( 46, 87)( 47, 86)( 48, 85)
( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 80)( 54, 79)( 55, 78)( 56, 77)
( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 61, 71)( 62, 72)( 63, 69)( 64, 70);;
s1 := (  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 26)( 18, 25)( 19, 28)( 20, 27)
( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 41)( 34, 42)( 35, 43)( 36, 44)
( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 50)( 51, 52)( 53, 56)( 54, 55)
( 57, 58)( 59, 60)( 61, 64)( 62, 63)( 65,121)( 66,122)( 67,123)( 68,124)
( 69,127)( 70,128)( 71,125)( 72,126)( 73,113)( 74,114)( 75,115)( 76,116)
( 77,119)( 78,120)( 79,117)( 80,118)( 81, 97)( 82, 98)( 83, 99)( 84,100)
( 85,103)( 86,104)( 87,101)( 88,102)( 89,105)( 90,106)( 91,107)( 92,108)
( 93,111)( 94,112)( 95,109)( 96,110);;
s2 := (  1, 95)(  2, 96)(  3, 93)(  4, 94)(  5, 91)(  6, 92)(  7, 89)(  8, 90)
(  9, 15)( 10, 16)( 11, 13)( 12, 14)( 17, 55)( 18, 56)( 19, 53)( 20, 54)
( 21, 51)( 22, 52)( 23, 49)( 24, 50)( 25,103)( 26,104)( 27,101)( 28,102)
( 29, 99)( 30,100)( 31, 97)( 32, 98)( 33,127)( 34,128)( 35,125)( 36,126)
( 37,123)( 38,124)( 39,121)( 40,122)( 41, 48)( 42, 47)( 43, 46)( 44, 45)
( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)( 64, 65)
( 73,111)( 74,112)( 75,109)( 76,110)( 77,107)( 78,108)( 79,105)( 80,106)
( 81, 88)( 82, 87)( 83, 86)( 84, 85)(113,119)(114,120)(115,117)(116,118);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(128)!(  1,123)(  2,124)(  3,121)(  4,122)(  5,127)(  6,128)(  7,125)
(  8,126)(  9,116)( 10,115)( 11,114)( 12,113)( 13,120)( 14,119)( 15,118)
( 16,117)( 17,108)( 18,107)( 19,106)( 20,105)( 21,112)( 22,111)( 23,110)
( 24,109)( 25, 99)( 26,100)( 27, 97)( 28, 98)( 29,103)( 30,104)( 31,101)
( 32,102)( 33, 91)( 34, 92)( 35, 89)( 36, 90)( 37, 95)( 38, 96)( 39, 93)
( 40, 94)( 41, 84)( 42, 83)( 43, 82)( 44, 81)( 45, 88)( 46, 87)( 47, 86)
( 48, 85)( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 80)( 54, 79)( 55, 78)
( 56, 77)( 57, 67)( 58, 68)( 59, 65)( 60, 66)( 61, 71)( 62, 72)( 63, 69)
( 64, 70);
s1 := Sym(128)!(  5,  7)(  6,  8)( 13, 15)( 14, 16)( 17, 26)( 18, 25)( 19, 28)
( 20, 27)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 41)( 34, 42)( 35, 43)
( 36, 44)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 50)( 51, 52)( 53, 56)
( 54, 55)( 57, 58)( 59, 60)( 61, 64)( 62, 63)( 65,121)( 66,122)( 67,123)
( 68,124)( 69,127)( 70,128)( 71,125)( 72,126)( 73,113)( 74,114)( 75,115)
( 76,116)( 77,119)( 78,120)( 79,117)( 80,118)( 81, 97)( 82, 98)( 83, 99)
( 84,100)( 85,103)( 86,104)( 87,101)( 88,102)( 89,105)( 90,106)( 91,107)
( 92,108)( 93,111)( 94,112)( 95,109)( 96,110);
s2 := Sym(128)!(  1, 95)(  2, 96)(  3, 93)(  4, 94)(  5, 91)(  6, 92)(  7, 89)
(  8, 90)(  9, 15)( 10, 16)( 11, 13)( 12, 14)( 17, 55)( 18, 56)( 19, 53)
( 20, 54)( 21, 51)( 22, 52)( 23, 49)( 24, 50)( 25,103)( 26,104)( 27,101)
( 28,102)( 29, 99)( 30,100)( 31, 97)( 32, 98)( 33,127)( 34,128)( 35,125)
( 36,126)( 37,123)( 38,124)( 39,121)( 40,122)( 41, 48)( 42, 47)( 43, 46)
( 44, 45)( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)
( 64, 65)( 73,111)( 74,112)( 75,109)( 76,110)( 77,107)( 78,108)( 79,105)
( 80,106)( 81, 88)( 82, 87)( 83, 86)( 84, 85)(113,119)(114,120)(115,117)
(116,118);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
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