Polytope of Type {11,2,3}

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

to this polytope