Polytope of Type {5,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,20}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116393)
Rank : 3
Schlafli Type : {5,20}
Number of vertices, edges, etc : 32, 320, 128
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 20
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 : {5,10}*640, {5,20}*640a, {5,20}*640b
   4-fold quotients : {5,5}*320, {5,10}*320a, {5,10}*320b
   8-fold quotients : {5,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope