Polytope of Type {4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20}*1280c
if this polytope has a name.
Group : SmallGroup(1280,1116447)
Rank : 3
Schlafli Type : {4,20}
Number of vertices, edges, etc : 32, 320, 160
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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}*640b, {4,20}*640c, {4,10}*640b
   4-fold quotients : {4,5}*320, {4,10}*320a, {4,10}*320b
   8-fold quotients : {4,5}*160
   16-fold quotients : {2,20}*80
   32-fold quotients : {2,10}*40
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope