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Polytope of Type {8,2,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,11}*352
if this polytope has a name.
Group : SmallGroup(352,105)
Rank : 4
Schlafli Type : {8,2,11}
Number of vertices, edges, etc : 8, 8, 11, 11
Order of s0s1s2s3 : 88
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,11,2} of size 704
Vertex Figure Of :
   {2,8,2,11} of size 704
   {4,8,2,11} of size 1408
   {4,8,2,11} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,11}*176
   4-fold quotients : {2,2,11}*88
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,2,11}*704, {8,2,22}*704
   3-fold covers : {24,2,11}*1056, {8,2,33}*1056
   4-fold covers : {32,2,11}*1408, {8,4,22}*1408a, {8,2,44}*1408, {16,2,22}*1408
   5-fold covers : {40,2,11}*1760, {8,2,55}*1760
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,15)(16,17)(18,19);;
s3 := ( 9,10)(11,12)(13,14)(15,16)(17,18);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(19)!(2,3)(4,5)(6,7);
s1 := Sym(19)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(19)!(10,11)(12,13)(14,15)(16,17)(18,19);
s3 := Sym(19)!( 9,10)(11,12)(13,14)(15,16)(17,18);
poly := sub<Sym(19)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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