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

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

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

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