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

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

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