Polytope of Type {2,6,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,15}*1080
if this polytope has a name.
Group : SmallGroup(1080,337)
Rank : 4
Schlafli Type : {2,6,15}
Number of vertices, edges, etc : 2, 18, 135, 45
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,6,15}*360
   5-fold quotients : {2,6,3}*216
   9-fold quotients : {2,2,15}*120
   15-fold quotients : {2,6,3}*72
   27-fold quotients : {2,2,5}*40
   45-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*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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