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Polytope of Type {6,10,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,3}*720
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 4
Schlafli Type : {6,10,3}
Number of vertices, edges, etc : 6, 60, 30, 6
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,10,3,2} of size 1440
Vertex Figure Of :
   {2,6,10,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,3}*240a
   6-fold quotients : {2,5,3}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,10,3}*1440, {6,10,3}*1440, {6,10,6}*1440c, {6,10,6}*1440d
Permutation Representation (GAP) :
s0 := (4,5);;
s1 := ( 1, 2)( 3, 4)( 7, 8)( 9,10);;
s2 := (6,7)(8,9);;
s3 := ( 7,10)( 8, 9);;
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, s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(4,5);
s1 := Sym(10)!( 1, 2)( 3, 4)( 7, 8)( 9,10);
s2 := Sym(10)!(6,7)(8,9);
s3 := Sym(10)!( 7,10)( 8, 9);
poly := sub<Sym(10)|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, 
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >; 
 
References : None.
to this polytope