Polytope of Type {20,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope