Polytope of Type {20,8}

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

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

Permutation Representation (Magma) :

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

References : None.
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