Polytope of Type {2,2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,15,6}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 5
Schlafli Type : {2,2,15,6}
Number of vertices, edges, etc : 2, 2, 15, 45, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,15,6,2} of size 1440
Vertex Figure Of :
   {2,2,2,15,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,15,2}*240
   5-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,2,5,2}*80
   15-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,15,6}*1440, {2,2,30,6}*1440c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)
(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)
(34,41);;
s3 := ( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)(14,22)
(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)
(47,49);;
s4 := (20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)
(30,45)(31,46)(32,47)(33,48)(34,49);;
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(49)!(1,2);
s1 := Sym(49)!(3,4);
s2 := Sym(49)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)
(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)
(33,42)(34,41);
s3 := Sym(49)!( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)
(14,22)(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)
(45,46)(47,49);
s4 := Sym(49)!(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)
(29,44)(30,45)(31,46)(32,47)(33,48)(34,49);
poly := sub<Sym(49)|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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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