Polytope of Type {2,2,4,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,60}*1920a
if this polytope has a name.
Group : SmallGroup(1920,205027)
Rank : 5
Schlafli Type : {2,2,4,60}
Number of vertices, edges, etc : 2, 2, 4, 120, 60
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {2,2,2,60}*960, {2,2,4,30}*960a
   3-fold quotients : {2,2,4,20}*640
   4-fold quotients : {2,2,2,30}*480
   5-fold quotients : {2,2,4,12}*384a
   6-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320
   8-fold quotients : {2,2,2,15}*240
   10-fold quotients : {2,2,2,12}*192, {2,2,4,6}*192a
   12-fold quotients : {2,2,2,10}*160
   15-fold quotients : {2,2,4,4}*128
   20-fold quotients : {2,2,2,6}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)
( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 78, 93)( 79, 94)( 95,110)
( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)
(104,119)(105,120)(106,121)(107,122)(108,123)(109,124);;
s3 := (  5, 65)(  6, 69)(  7, 68)(  8, 67)(  9, 66)( 10, 75)( 11, 79)( 12, 78)
( 13, 77)( 14, 76)( 15, 70)( 16, 74)( 17, 73)( 18, 72)( 19, 71)( 20, 80)
( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 90)( 26, 94)( 27, 93)( 28, 92)
( 29, 91)( 30, 85)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 95)( 36, 99)
( 37, 98)( 38, 97)( 39, 96)( 40,105)( 41,109)( 42,108)( 43,107)( 44,106)
( 45,100)( 46,104)( 47,103)( 48,102)( 49,101)( 50,110)( 51,114)( 52,113)
( 53,112)( 54,111)( 55,120)( 56,124)( 57,123)( 58,122)( 59,121)( 60,115)
( 61,119)( 62,118)( 63,117)( 64,116);;
s4 := (  5, 11)(  6, 10)(  7, 14)(  8, 13)(  9, 12)( 15, 16)( 17, 19)( 20, 26)
( 21, 25)( 22, 29)( 23, 28)( 24, 27)( 30, 31)( 32, 34)( 35, 41)( 36, 40)
( 37, 44)( 38, 43)( 39, 42)( 45, 46)( 47, 49)( 50, 56)( 51, 55)( 52, 59)
( 53, 58)( 54, 57)( 60, 61)( 62, 64)( 65,101)( 66,100)( 67,104)( 68,103)
( 69,102)( 70, 96)( 71, 95)( 72, 99)( 73, 98)( 74, 97)( 75,106)( 76,105)
( 77,109)( 78,108)( 79,107)( 80,116)( 81,115)( 82,119)( 83,118)( 84,117)
( 85,111)( 86,110)( 87,114)( 88,113)( 89,112)( 90,121)( 91,120)( 92,124)
( 93,123)( 94,122);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 78, 93)( 79, 94)
( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)
(103,118)(104,119)(105,120)(106,121)(107,122)(108,123)(109,124);
s3 := Sym(124)!(  5, 65)(  6, 69)(  7, 68)(  8, 67)(  9, 66)( 10, 75)( 11, 79)
( 12, 78)( 13, 77)( 14, 76)( 15, 70)( 16, 74)( 17, 73)( 18, 72)( 19, 71)
( 20, 80)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 90)( 26, 94)( 27, 93)
( 28, 92)( 29, 91)( 30, 85)( 31, 89)( 32, 88)( 33, 87)( 34, 86)( 35, 95)
( 36, 99)( 37, 98)( 38, 97)( 39, 96)( 40,105)( 41,109)( 42,108)( 43,107)
( 44,106)( 45,100)( 46,104)( 47,103)( 48,102)( 49,101)( 50,110)( 51,114)
( 52,113)( 53,112)( 54,111)( 55,120)( 56,124)( 57,123)( 58,122)( 59,121)
( 60,115)( 61,119)( 62,118)( 63,117)( 64,116);
s4 := Sym(124)!(  5, 11)(  6, 10)(  7, 14)(  8, 13)(  9, 12)( 15, 16)( 17, 19)
( 20, 26)( 21, 25)( 22, 29)( 23, 28)( 24, 27)( 30, 31)( 32, 34)( 35, 41)
( 36, 40)( 37, 44)( 38, 43)( 39, 42)( 45, 46)( 47, 49)( 50, 56)( 51, 55)
( 52, 59)( 53, 58)( 54, 57)( 60, 61)( 62, 64)( 65,101)( 66,100)( 67,104)
( 68,103)( 69,102)( 70, 96)( 71, 95)( 72, 99)( 73, 98)( 74, 97)( 75,106)
( 76,105)( 77,109)( 78,108)( 79,107)( 80,116)( 81,115)( 82,119)( 83,118)
( 84,117)( 85,111)( 86,110)( 87,114)( 88,113)( 89,112)( 90,121)( 91,120)
( 92,124)( 93,123)( 94,122);
poly := sub<Sym(124)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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