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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,60}*1440
if this polytope has a name.
Group : SmallGroup(1440,5676)
Rank : 5
Schlafli Type : {2,3,2,60}
Number of vertices, edges, etc : 2, 3, 3, 60, 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 : {2,3,2,30}*720
   3-fold quotients : {2,3,2,20}*480
   4-fold quotients : {2,3,2,15}*360
   5-fold quotients : {2,3,2,12}*288
   6-fold quotients : {2,3,2,10}*240
   10-fold quotients : {2,3,2,6}*144
   12-fold quotients : {2,3,2,5}*120
   15-fold quotients : {2,3,2,4}*96
   20-fold quotients : {2,3,2,3}*72
   30-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 7, 8)( 9,10)(11,12)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24)(26,27)
(28,29)(30,31)(32,41)(33,40)(34,39)(35,38)(36,43)(37,42)(44,47)(45,46)(48,51)
(49,50)(52,53)(54,61)(55,60)(56,59)(57,58)(62,65)(63,64);;
s4 := ( 6,32)( 7,22)( 8,48)( 9,16)(10,34)(11,14)(12,54)(13,38)(15,24)(17,44)
(18,30)(19,50)(20,28)(21,62)(23,36)(25,56)(26,33)(27,55)(29,40)(31,58)(35,46)
(37,45)(39,52)(41,64)(42,49)(43,63)(47,57)(51,60)(53,59)(61,65);;
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, s1*s2*s1*s2*s1*s2, 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(65)!(1,2);
s1 := Sym(65)!(4,5);
s2 := Sym(65)!(3,4);
s3 := Sym(65)!( 7, 8)( 9,10)(11,12)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24)
(26,27)(28,29)(30,31)(32,41)(33,40)(34,39)(35,38)(36,43)(37,42)(44,47)(45,46)
(48,51)(49,50)(52,53)(54,61)(55,60)(56,59)(57,58)(62,65)(63,64);
s4 := Sym(65)!( 6,32)( 7,22)( 8,48)( 9,16)(10,34)(11,14)(12,54)(13,38)(15,24)
(17,44)(18,30)(19,50)(20,28)(21,62)(23,36)(25,56)(26,33)(27,55)(29,40)(31,58)
(35,46)(37,45)(39,52)(41,64)(42,49)(43,63)(47,57)(51,60)(53,59)(61,65);
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, 
s1*s2*s1*s2*s1*s2, 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 >;

to this polytope