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

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

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