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Polytope of Type {12,2,15,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,15,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,5675)
Rank : 5
Schlafli Type : {12,2,15,2}
Number of vertices, edges, etc : 12, 12, 15, 15, 2
Order of s0s1s2s3s4 : 60
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) :
   2-fold quotients : {6,2,15,2}*720
   3-fold quotients : {12,2,5,2}*480, {4,2,15,2}*480
   4-fold quotients : {3,2,15,2}*360
   5-fold quotients : {12,2,3,2}*288
   6-fold quotients : {6,2,5,2}*240, {2,2,15,2}*240
   9-fold quotients : {4,2,5,2}*160
   10-fold quotients : {6,2,3,2}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {4,2,3,2}*96
   18-fold quotients : {2,2,5,2}*80
   20-fold quotients : {3,2,3,2}*72
   30-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s3 := (13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s4 := (28,29);;
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, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(29)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(29)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(29)!(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s3 := Sym(29)!(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
s4 := Sym(29)!(28,29);
poly := sub<Sym(29)|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, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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