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Polytope of Type {6,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,6}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 4
Schlafli Type : {6,10,6}
Number of vertices, edges, etc : 6, 60, 60, 12
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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 : {6,10,3}*720
   3-fold quotients : {2,10,6}*480e
   6-fold quotients : {2,5,6}*240b, {2,10,3}*240a
   12-fold quotients : {2,5,3}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (12,16)(13,15);;
s1 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,12)(13,16)(14,15);;
s2 := ( 1, 4)( 2, 3)( 5, 7)( 6, 8)( 9,10);;
s3 := ( 3,10)( 4, 9)( 5, 8)( 6, 7);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!(12,16)(13,15);
s1 := Sym(16)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,12)(13,16)(14,15);
s2 := Sym(16)!( 1, 4)( 2, 3)( 5, 7)( 6, 8)( 9,10);
s3 := Sym(16)!( 3,10)( 4, 9)( 5, 8)( 6, 7);
poly := sub<Sym(16)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >; 
 
References : None.
to this polytope