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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15,2,2}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 5
Schlafli Type : {6,15,2,2}
Number of vertices, edges, etc : 6, 45, 15, 2, 2
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,15,2,2,2} of size 1440
Vertex Figure Of :
   {2,6,15,2,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,15,2,2}*240
   5-fold quotients : {6,3,2,2}*144
   9-fold quotients : {2,5,2,2}*80
   15-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,15,2,4}*1440, {6,30,2,2}*1440c
Permutation Representation (GAP) :
s0 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)
(26,41)(27,42)(28,43)(29,44)(30,45);;
s1 := ( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)(10,27)
(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)
(40,42);;
s2 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,37)(17,36)(18,40)
(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(26,42)(27,41)(28,45)(29,44)
(30,43);;
s3 := (46,47);;
s4 := (48,49);;
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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(49)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)
(25,40)(26,41)(27,42)(28,43)(29,44)(30,45);
s1 := Sym(49)!( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)
(10,27)(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)
(39,43)(40,42);
s2 := Sym(49)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,37)(17,36)
(18,40)(19,39)(20,38)(21,32)(22,31)(23,35)(24,34)(25,33)(26,42)(27,41)(28,45)
(29,44)(30,43);
s3 := Sym(49)!(46,47);
s4 := Sym(49)!(48,49);
poly := sub<Sym(49)|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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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