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Polytope of Type {3,2,11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,11}*132
if this polytope has a name.
Group : SmallGroup(132,5)
Rank : 4
Schlafli Type : {3,2,11}
Number of vertices, edges, etc : 3, 3, 11, 11
Order of s0s1s2s3 : 33
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,11,2} of size 264
Vertex Figure Of :
   {2,3,2,11} of size 264
   {3,3,2,11} of size 528
   {4,3,2,11} of size 528
   {6,3,2,11} of size 792
   {4,3,2,11} of size 1056
   {6,3,2,11} of size 1056
   {5,3,2,11} of size 1320
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,22}*264, {6,2,11}*264
   3-fold covers : {9,2,11}*396, {3,2,33}*396
   4-fold covers : {12,2,11}*528, {3,2,44}*528, {6,2,22}*528
   5-fold covers : {15,2,11}*660, {3,2,55}*660
   6-fold covers : {9,2,22}*792, {18,2,11}*792, {3,6,22}*792, {3,2,66}*792, {6,2,33}*792
   7-fold covers : {21,2,11}*924, {3,2,77}*924
   8-fold covers : {24,2,11}*1056, {3,2,88}*1056, {12,2,22}*1056, {6,2,44}*1056, {6,4,22}*1056, {3,4,22}*1056
   9-fold covers : {27,2,11}*1188, {3,2,99}*1188, {9,2,33}*1188, {3,6,33}*1188
   10-fold covers : {15,2,22}*1320, {30,2,11}*1320, {3,2,110}*1320, {6,2,55}*1320
   11-fold covers : {3,2,121}*1452, {33,2,11}*1452
   12-fold covers : {36,2,11}*1584, {9,2,44}*1584, {18,2,22}*1584, {3,6,44}*1584, {12,2,33}*1584, {3,2,132}*1584, {6,6,22}*1584a, {6,6,22}*1584c, {6,2,66}*1584
   13-fold covers : {39,2,11}*1716, {3,2,143}*1716
   14-fold covers : {21,2,22}*1848, {42,2,11}*1848, {3,2,154}*1848, {6,2,77}*1848
   15-fold covers : {45,2,11}*1980, {9,2,55}*1980, {15,2,33}*1980, {3,2,165}*1980
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
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, 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(14)!(2,3);
s1 := Sym(14)!(1,2);
s2 := Sym(14)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s3 := Sym(14)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
poly := sub<Sym(14)|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, 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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