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Polytope of Type {2,60,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,2,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,5676)
Rank : 5
Schlafli Type : {2,60,2,3}
Number of vertices, edges, etc : 2, 60, 60, 3, 3
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 : {2,30,2,3}*720
   3-fold quotients : {2,20,2,3}*480
   4-fold quotients : {2,15,2,3}*360
   5-fold quotients : {2,12,2,3}*288
   6-fold quotients : {2,10,2,3}*240
   10-fold quotients : {2,6,2,3}*144
   12-fold quotients : {2,5,2,3}*120
   15-fold quotients : {2,4,2,3}*96
   20-fold quotients : {2,3,2,3}*72
   30-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(11,16)(12,15)(13,18)(14,17)(19,22)(20,21)(23,24)
(25,26)(27,28)(29,38)(30,37)(31,36)(32,35)(33,40)(34,39)(41,44)(42,43)(45,48)
(46,47)(49,50)(51,58)(52,57)(53,56)(54,55)(59,62)(60,61);;
s2 := ( 3,29)( 4,19)( 5,45)( 6,13)( 7,31)( 8,11)( 9,51)(10,35)(12,21)(14,41)
(15,27)(16,47)(17,25)(18,59)(20,33)(22,53)(23,30)(24,52)(26,37)(28,55)(32,43)
(34,42)(36,49)(38,61)(39,46)(40,60)(44,54)(48,57)(50,56)(58,62);;
s3 := (64,65);;
s4 := (63,64);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 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(65)!(1,2);
s1 := Sym(65)!( 4, 5)( 6, 7)( 8, 9)(11,16)(12,15)(13,18)(14,17)(19,22)(20,21)
(23,24)(25,26)(27,28)(29,38)(30,37)(31,36)(32,35)(33,40)(34,39)(41,44)(42,43)
(45,48)(46,47)(49,50)(51,58)(52,57)(53,56)(54,55)(59,62)(60,61);
s2 := Sym(65)!( 3,29)( 4,19)( 5,45)( 6,13)( 7,31)( 8,11)( 9,51)(10,35)(12,21)
(14,41)(15,27)(16,47)(17,25)(18,59)(20,33)(22,53)(23,30)(24,52)(26,37)(28,55)
(32,43)(34,42)(36,49)(38,61)(39,46)(40,60)(44,54)(48,57)(50,56)(58,62);
s3 := Sym(65)!(64,65);
s4 := Sym(65)!(63,64);
poly := sub<Sym(65)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, 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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