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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,15,2}*1080
if this polytope has a name.
Group : SmallGroup(1080,337)
Rank : 5
Schlafli Type : {3,6,15,2}
Number of vertices, edges, etc : 3, 9, 45, 15, 2
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 : {3,6,3,2}*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)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,33)(34,36)(37,39)(40,42)(43,45);;
s2 := ( 1,16)( 2,18)( 3,17)( 4,28)( 5,30)( 6,29)( 7,25)( 8,27)( 9,26)(10,22)
(11,24)(12,23)(13,19)(14,21)(15,20)(32,33)(34,43)(35,45)(36,44)(37,40)(38,42)
(39,41);;
s3 := ( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,34)(17,36)(18,35)
(19,31)(20,33)(21,32)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,37)(29,39)
(30,38);;
s4 := (46,47);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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(47)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45);
s1 := Sym(47)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,17)(19,20)(22,23)(25,26)
(28,29)(31,33)(34,36)(37,39)(40,42)(43,45);
s2 := Sym(47)!( 1,16)( 2,18)( 3,17)( 4,28)( 5,30)( 6,29)( 7,25)( 8,27)( 9,26)
(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(32,33)(34,43)(35,45)(36,44)(37,40)
(38,42)(39,41);
s3 := Sym(47)!( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,34)(17,36)
(18,35)(19,31)(20,33)(21,32)(22,43)(23,45)(24,44)(25,40)(26,42)(27,41)(28,37)
(29,39)(30,38);
s4 := Sym(47)!(46,47);
poly := sub<Sym(47)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
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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