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Polytope of Type {2,60,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,4}*960a
if this polytope has a name.
Group : SmallGroup(960,10441)
Rank : 4
Schlafli Type : {2,60,4}
Number of vertices, edges, etc : 2, 60, 120, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,60,4,2} of size 1920
Vertex Figure Of :
   {2,2,60,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,60,2}*480, {2,30,4}*480a
   3-fold quotients : {2,20,4}*320
   4-fold quotients : {2,30,2}*240
   5-fold quotients : {2,12,4}*192a
   6-fold quotients : {2,20,2}*160, {2,10,4}*160
   8-fold quotients : {2,15,2}*120
   10-fold quotients : {2,12,2}*96, {2,6,4}*96a
   12-fold quotients : {2,10,2}*80
   15-fold quotients : {2,4,4}*64
   20-fold quotients : {2,6,2}*48
   24-fold quotients : {2,5,2}*40
   30-fold quotients : {2,2,4}*32, {2,4,2}*32
   40-fold quotients : {2,3,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60,4}*1920a, {2,60,8}*1920a, {2,120,4}*1920a, {2,60,8}*1920b, {2,120,4}*1920b, {2,60,4}*1920a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)( 35, 36)
( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)( 53, 58)
( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 93)( 64, 97)( 65, 96)( 66, 95)
( 67, 94)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)( 73, 98)( 74,102)
( 75,101)( 76,100)( 77, 99)( 78,108)( 79,112)( 80,111)( 81,110)( 82,109)
( 83,118)( 84,122)( 85,121)( 86,120)( 87,119)( 88,113)( 89,117)( 90,116)
( 91,115)( 92,114);;
s2 := (  3, 69)(  4, 68)(  5, 72)(  6, 71)(  7, 70)(  8, 64)(  9, 63)( 10, 67)
( 11, 66)( 12, 65)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)( 18, 84)
( 19, 83)( 20, 87)( 21, 86)( 22, 85)( 23, 79)( 24, 78)( 25, 82)( 26, 81)
( 27, 80)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33, 99)( 34, 98)
( 35,102)( 36,101)( 37,100)( 38, 94)( 39, 93)( 40, 97)( 41, 96)( 42, 95)
( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48,114)( 49,113)( 50,117)
( 51,116)( 52,115)( 53,109)( 54,108)( 55,112)( 56,111)( 57,110)( 58,119)
( 59,118)( 60,122)( 61,121)( 62,120);;
s3 := ( 63, 78)( 64, 79)( 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)( 93,108)
( 94,109)( 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);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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(122)!(1,2);
s1 := Sym(122)!(  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 34, 37)
( 35, 36)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 93)( 64, 97)( 65, 96)
( 66, 95)( 67, 94)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)( 73, 98)
( 74,102)( 75,101)( 76,100)( 77, 99)( 78,108)( 79,112)( 80,111)( 81,110)
( 82,109)( 83,118)( 84,122)( 85,121)( 86,120)( 87,119)( 88,113)( 89,117)
( 90,116)( 91,115)( 92,114);
s2 := Sym(122)!(  3, 69)(  4, 68)(  5, 72)(  6, 71)(  7, 70)(  8, 64)(  9, 63)
( 10, 67)( 11, 66)( 12, 65)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)
( 18, 84)( 19, 83)( 20, 87)( 21, 86)( 22, 85)( 23, 79)( 24, 78)( 25, 82)
( 26, 81)( 27, 80)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33, 99)
( 34, 98)( 35,102)( 36,101)( 37,100)( 38, 94)( 39, 93)( 40, 97)( 41, 96)
( 42, 95)( 43,104)( 44,103)( 45,107)( 46,106)( 47,105)( 48,114)( 49,113)
( 50,117)( 51,116)( 52,115)( 53,109)( 54,108)( 55,112)( 56,111)( 57,110)
( 58,119)( 59,118)( 60,122)( 61,121)( 62,120);
s3 := Sym(122)!( 63, 78)( 64, 79)( 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)
( 93,108)( 94,109)( 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);
poly := sub<Sym(122)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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*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*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 >; 
 

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