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Polytope of Type {2,2,2,6,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,6,5}*960c
if this polytope has a name.
Group : SmallGroup(960,11356)
Rank : 6
Schlafli Type : {2,2,2,6,5}
Number of vertices, edges, etc : 2, 2, 2, 12, 30, 10
Order of s0s1s2s3s4s5 : 10
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,6,5,2} of size 1920
Vertex Figure Of :
   {2,2,2,2,6,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,3,5}*480
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,6,5}*1920c, {4,2,2,6,5}*1920c, {2,2,2,6,5}*1920b, {2,2,2,6,10}*1920c, {2,2,2,6,10}*1920f
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7, 9)( 8,14)(10,18)(11,13)(12,15)(16,17);;
s4 := ( 8, 9)(10,12)(11,15)(14,17);;
s5 := ( 8,15)(10,18)(11,13)(12,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4, 
s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!(1,2);
s1 := Sym(18)!(3,4);
s2 := Sym(18)!(5,6);
s3 := Sym(18)!( 7, 9)( 8,14)(10,18)(11,13)(12,15)(16,17);
s4 := Sym(18)!( 8, 9)(10,12)(11,15)(14,17);
s5 := Sym(18)!( 8,15)(10,18)(11,13)(12,14);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4, 
s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4*s5*s3*s4*s5 >; 
 

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