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Polytope of Type {15,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*720
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 36, 180, 24
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {15,10,2} of size 1440
Vertex Figure Of :
   {2,15,10} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,10}*360
   3-fold quotients : {5,10}*240
   6-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b
   12-fold quotients : {5,5}*60
   60-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,20}*1440a, {30,10}*1440
Permutation Representation (GAP) :
s0 := ( 4, 5)( 7, 8)( 9,10);;
s1 := (3,4)(6,7)(8,9);;
s2 := ( 1, 2)( 7, 9)( 8,10);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!( 4, 5)( 7, 8)( 9,10);
s1 := Sym(10)!(3,4)(6,7)(8,9);
s2 := Sym(10)!( 1, 2)( 7, 9)( 8,10);
poly := sub<Sym(10)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope