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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,6}*480b
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 5
Schlafli Type : {2,2,5,6}
Number of vertices, edges, etc : 2, 2, 10, 30, 12
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,5,6,2} of size 960
Vertex Figure Of :
   {2,2,2,5,6} of size 960
   {3,2,2,5,6} of size 1440
   {4,2,2,5,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,5,3}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,5,6}*960b, {2,2,5,6}*960b, {2,2,10,6}*960e, {2,2,10,6}*960f
   3-fold covers : {2,2,15,6}*1440, {6,2,5,6}*1440b
   4-fold covers : {8,2,5,6}*1920b, {2,2,20,6}*1920b, {2,2,20,6}*1920c, {2,4,10,6}*1920c, {4,2,5,6}*1920b, {4,2,10,6}*1920e, {4,2,10,6}*1920f, {2,2,10,6}*1920b, {2,2,5,12}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,13)( 8,16)( 9,11)(10,12);;
s3 := ( 7, 9)( 8,15)(10,16)(11,13);;
s4 := ( 5,15)( 6,13)( 7,14)( 8, 9)(10,12)(11,16);;
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*s1*s0*s1, 
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(3,4);
s2 := Sym(16)!( 6,13)( 8,16)( 9,11)(10,12);
s3 := Sym(16)!( 7, 9)( 8,15)(10,16)(11,13);
s4 := Sym(16)!( 5,15)( 6,13)( 7,14)( 8, 9)(10,12)(11,16);
poly := sub<Sym(16)|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*s1*s0*s1, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3 >; 
 

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