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Polytope of Type {2,2,2,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,11}*176
if this polytope has a name.
Group : SmallGroup(176,41)
Rank : 5
Schlafli Type : {2,2,2,11}
Number of vertices, edges, etc : 2, 2, 2, 11, 11
Order of s0s1s2s3s4 : 22
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,11,2} of size 352
Vertex Figure Of :
   {2,2,2,2,11} of size 352
   {3,2,2,2,11} of size 528
   {4,2,2,2,11} of size 704
   {5,2,2,2,11} of size 880
   {6,2,2,2,11} of size 1056
   {7,2,2,2,11} of size 1232
   {8,2,2,2,11} of size 1408
   {9,2,2,2,11} of size 1584
   {10,2,2,2,11} of size 1760
   {11,2,2,2,11} of size 1936
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,11}*352, {4,2,2,11}*352, {2,2,2,22}*352
   3-fold covers : {2,6,2,11}*528, {6,2,2,11}*528, {2,2,2,33}*528
   4-fold covers : {4,4,2,11}*704, {2,8,2,11}*704, {8,2,2,11}*704, {2,2,2,44}*704, {2,2,4,22}*704, {2,4,2,22}*704, {4,2,2,22}*704
   5-fold covers : {2,10,2,11}*880, {10,2,2,11}*880, {2,2,2,55}*880
   6-fold covers : {2,12,2,11}*1056, {12,2,2,11}*1056, {4,6,2,11}*1056a, {6,4,2,11}*1056a, {2,4,2,33}*1056, {4,2,2,33}*1056, {2,2,6,22}*1056, {2,6,2,22}*1056, {6,2,2,22}*1056, {2,2,2,66}*1056
   7-fold covers : {2,14,2,11}*1232, {14,2,2,11}*1232, {2,2,2,77}*1232
   8-fold covers : {4,8,2,11}*1408a, {8,4,2,11}*1408a, {4,8,2,11}*1408b, {8,4,2,11}*1408b, {4,4,2,11}*1408, {2,16,2,11}*1408, {16,2,2,11}*1408, {2,4,4,22}*1408, {4,4,2,22}*1408, {2,2,4,44}*1408, {4,2,4,22}*1408, {2,4,2,44}*1408, {4,2,2,44}*1408, {2,2,8,22}*1408, {2,8,2,22}*1408, {8,2,2,22}*1408, {2,2,2,88}*1408
   9-fold covers : {2,18,2,11}*1584, {18,2,2,11}*1584, {2,2,2,99}*1584, {6,6,2,11}*1584a, {6,6,2,11}*1584b, {6,6,2,11}*1584c, {2,2,6,33}*1584, {2,6,2,33}*1584, {6,2,2,33}*1584
   10-fold covers : {2,20,2,11}*1760, {20,2,2,11}*1760, {4,10,2,11}*1760, {10,4,2,11}*1760, {2,4,2,55}*1760, {4,2,2,55}*1760, {2,2,10,22}*1760, {2,10,2,22}*1760, {10,2,2,22}*1760, {2,2,2,110}*1760
   11-fold covers : {2,2,2,121}*1936, {2,2,22,11}*1936, {2,22,2,11}*1936, {22,2,2,11}*1936
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s4 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
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, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(17)!(1,2);
s1 := Sym(17)!(3,4);
s2 := Sym(17)!(5,6);
s3 := Sym(17)!( 8, 9)(10,11)(12,13)(14,15)(16,17);
s4 := Sym(17)!( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(17)|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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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