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

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

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