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Polytope of Type {3,2,5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,5,5}*720
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 5
Schlafli Type : {3,2,5,5}
Number of vertices, edges, etc : 3, 3, 12, 30, 12
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,5,5,2} of size 1440
Vertex Figure Of :
   {2,3,2,5,5} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,5,5}*360
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,5,10}*1440, {3,2,10,5}*1440, {6,2,5,5}*1440
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,12)( 7,15)( 8,10)( 9,11);;
s3 := ( 6, 8)( 7,14)( 9,15)(10,12);;
s4 := ( 4,14)( 6,13)( 7,10)( 8,15);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!(2,3);
s1 := Sym(15)!(1,2);
s2 := Sym(15)!( 5,12)( 7,15)( 8,10)( 9,11);
s3 := Sym(15)!( 6, 8)( 7,14)( 9,15)(10,12);
s4 := Sym(15)!( 4,14)( 6,13)( 7,10)( 8,15);
poly := sub<Sym(15)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 >; 
 

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