Polytope of Type {3,2,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,15,6}*1080
if this polytope has a name.
Group : SmallGroup(1080,539)
Rank : 5
Schlafli Type : {3,2,15,6}
Number of vertices, edges, etc : 3, 3, 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 : {3,2,15,2}*360
   5-fold quotients : {3,2,3,6}*216
   9-fold quotients : {3,2,5,2}*120
   15-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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