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Polytope of Type {11,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,7}*308
if this polytope has a name.
Group : SmallGroup(308,5)
Rank : 4
Schlafli Type : {11,2,7}
Number of vertices, edges, etc : 11, 11, 7, 7
Order of s0s1s2s3 : 77
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2,7,2} of size 616
Vertex Figure Of :
   {2,11,2,7} of size 616
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {11,2,14}*616, {22,2,7}*616
   3-fold covers : {11,2,21}*924, {33,2,7}*924
   4-fold covers : {11,2,28}*1232, {44,2,7}*1232, {22,2,14}*1232
   5-fold covers : {11,2,35}*1540, {55,2,7}*1540
   6-fold covers : {11,2,42}*1848, {22,2,21}*1848, {33,2,14}*1848, {66,2,7}*1848
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (13,14)(15,16)(17,18);;
s3 := (12,13)(14,15)(16,17);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(18)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(18)!(13,14)(15,16)(17,18);
s3 := Sym(18)!(12,13)(14,15)(16,17);
poly := sub<Sym(18)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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