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Polytope of Type {11,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,2}*88
if this polytope has a name.
Group : SmallGroup(88,11)
Rank : 4
Schlafli Type : {11,2,2}
Number of vertices, edges, etc : 11, 11, 2, 2
Order of s0s1s2s3 : 22
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2,2,2} of size 176
   {11,2,2,3} of size 264
   {11,2,2,4} of size 352
   {11,2,2,5} of size 440
   {11,2,2,6} of size 528
   {11,2,2,7} of size 616
   {11,2,2,8} of size 704
   {11,2,2,9} of size 792
   {11,2,2,10} of size 880
   {11,2,2,11} of size 968
   {11,2,2,12} of size 1056
   {11,2,2,13} of size 1144
   {11,2,2,14} of size 1232
   {11,2,2,15} of size 1320
   {11,2,2,16} of size 1408
   {11,2,2,17} of size 1496
   {11,2,2,18} of size 1584
   {11,2,2,19} of size 1672
   {11,2,2,20} of size 1760
   {11,2,2,21} of size 1848
   {11,2,2,22} of size 1936
Vertex Figure Of :
   {2,11,2,2} of size 176
   {22,11,2,2} of size 1936
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {11,2,4}*176, {22,2,2}*176
   3-fold covers : {11,2,6}*264, {33,2,2}*264
   4-fold covers : {11,2,8}*352, {44,2,2}*352, {22,2,4}*352, {22,4,2}*352
   5-fold covers : {11,2,10}*440, {55,2,2}*440
   6-fold covers : {11,2,12}*528, {33,2,4}*528, {22,2,6}*528, {22,6,2}*528, {66,2,2}*528
   7-fold covers : {11,2,14}*616, {77,2,2}*616
   8-fold covers : {11,2,16}*704, {44,4,2}*704, {44,2,4}*704, {22,4,4}*704, {88,2,2}*704, {22,2,8}*704, {22,8,2}*704
   9-fold covers : {11,2,18}*792, {99,2,2}*792, {33,2,6}*792, {33,6,2}*792
   10-fold covers : {11,2,20}*880, {55,2,4}*880, {22,2,10}*880, {22,10,2}*880, {110,2,2}*880
   11-fold covers : {121,2,2}*968, {11,2,22}*968, {11,22,2}*968
   12-fold covers : {11,2,24}*1056, {33,2,8}*1056, {22,2,12}*1056, {22,12,2}*1056, {44,2,6}*1056, {44,6,2}*1056a, {22,4,6}*1056, {22,6,4}*1056a, {132,2,2}*1056, {66,2,4}*1056, {66,4,2}*1056a, {33,6,2}*1056, {33,4,2}*1056
   13-fold covers : {11,2,26}*1144, {143,2,2}*1144
   14-fold covers : {11,2,28}*1232, {77,2,4}*1232, {22,2,14}*1232, {22,14,2}*1232, {154,2,2}*1232
   15-fold covers : {11,2,30}*1320, {33,2,10}*1320, {55,2,6}*1320, {165,2,2}*1320
   16-fold covers : {11,2,32}*1408, {44,4,4}*1408, {22,4,8}*1408a, {22,8,4}*1408a, {44,8,2}*1408a, {88,4,2}*1408a, {22,4,8}*1408b, {22,8,4}*1408b, {44,8,2}*1408b, {88,4,2}*1408b, {22,4,4}*1408, {44,4,2}*1408, {44,2,8}*1408, {88,2,4}*1408, {22,2,16}*1408, {22,16,2}*1408, {176,2,2}*1408
   17-fold covers : {11,2,34}*1496, {187,2,2}*1496
   18-fold covers : {11,2,36}*1584, {99,2,4}*1584, {22,2,18}*1584, {22,18,2}*1584, {198,2,2}*1584, {33,2,12}*1584, {33,6,4}*1584, {22,6,6}*1584a, {22,6,6}*1584b, {22,6,6}*1584c, {66,6,2}*1584a, {66,2,6}*1584, {66,6,2}*1584b, {66,6,2}*1584c
   19-fold covers : {11,2,38}*1672, {209,2,2}*1672
   20-fold covers : {11,2,40}*1760, {55,2,8}*1760, {22,2,20}*1760, {22,20,2}*1760, {44,2,10}*1760, {44,10,2}*1760, {22,4,10}*1760, {22,10,4}*1760, {220,2,2}*1760, {110,2,4}*1760, {110,4,2}*1760
   21-fold covers : {11,2,42}*1848, {33,2,14}*1848, {77,2,6}*1848, {231,2,2}*1848
   22-fold covers : {121,2,4}*1936, {242,2,2}*1936, {11,2,44}*1936, {11,22,4}*1936, {22,2,22}*1936, {22,22,2}*1936a, {22,22,2}*1936c
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 := (12,13);;
s3 := (14,15);;
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, 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(15)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(15)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(15)!(12,13);
s3 := Sym(15)!(14,15);
poly := sub<Sym(15)|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, 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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