Polytope of Type {5,2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,15,6}*1800
if this polytope has a name.
Group : SmallGroup(1800,678)
Rank : 5
Schlafli Type : {5,2,15,6}
Number of vertices, edges, etc : 5, 5, 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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,15,2}*600
   5-fold quotients : {5,2,3,6}*360
   9-fold quotients : {5,2,5,2}*200
   15-fold quotients : {5,2,3,2}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)(21,36)(22,40)(23,39)
(24,38)(25,37)(26,46)(27,50)(28,49)(29,48)(30,47)(31,41)(32,45)(33,44)(34,43)
(35,42);;
s3 := ( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,22)(12,21)(13,25)(14,24)(15,23)
(16,32)(17,31)(18,35)(19,34)(20,33)(36,42)(37,41)(38,45)(39,44)(40,43)(46,47)
(48,50);;
s4 := (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)(35,50);;
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*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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(50)!(2,3)(4,5);
s1 := Sym(50)!(1,2)(3,4);
s2 := Sym(50)!( 7,10)( 8, 9)(11,16)(12,20)(13,19)(14,18)(15,17)(21,36)(22,40)
(23,39)(24,38)(25,37)(26,46)(27,50)(28,49)(29,48)(30,47)(31,41)(32,45)(33,44)
(34,43)(35,42);
s3 := Sym(50)!( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,22)(12,21)(13,25)(14,24)
(15,23)(16,32)(17,31)(18,35)(19,34)(20,33)(36,42)(37,41)(38,45)(39,44)(40,43)
(46,47)(48,50);
s4 := Sym(50)!(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)(35,50);
poly := sub<Sym(50)|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*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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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