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Polytope of Type {11,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11,2,4}*176
if this polytope has a name.
Group : SmallGroup(176,31)
Rank : 4
Schlafli Type : {11,2,4}
Number of vertices, edges, etc : 11, 11, 4, 4
Order of s0s1s2s3 : 44
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2,4,2} of size 352
   {11,2,4,3} of size 528
   {11,2,4,4} of size 704
   {11,2,4,6} of size 1056
   {11,2,4,3} of size 1056
   {11,2,4,6} of size 1056
   {11,2,4,6} of size 1056
   {11,2,4,8} of size 1408
   {11,2,4,8} of size 1408
   {11,2,4,4} of size 1408
   {11,2,4,9} of size 1584
   {11,2,4,4} of size 1584
   {11,2,4,6} of size 1584
   {11,2,4,10} of size 1760
Vertex Figure Of :
   {2,11,2,4} of size 352
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,2,2}*88
Covers (Minimal Covers in Boldface) :
   2-fold covers : {11,2,8}*352, {22,2,4}*352
   3-fold covers : {11,2,12}*528, {33,2,4}*528
   4-fold covers : {11,2,16}*704, {44,2,4}*704, {22,4,4}*704, {22,2,8}*704
   5-fold covers : {11,2,20}*880, {55,2,4}*880
   6-fold covers : {11,2,24}*1056, {33,2,8}*1056, {22,2,12}*1056, {22,6,4}*1056a, {66,2,4}*1056
   7-fold covers : {11,2,28}*1232, {77,2,4}*1232
   8-fold covers : {11,2,32}*1408, {44,4,4}*1408, {22,4,8}*1408a, {22,8,4}*1408a, {22,4,8}*1408b, {22,8,4}*1408b, {22,4,4}*1408, {44,2,8}*1408, {88,2,4}*1408, {22,2,16}*1408
   9-fold covers : {11,2,36}*1584, {99,2,4}*1584, {33,2,12}*1584, {33,6,4}*1584
   10-fold covers : {11,2,40}*1760, {55,2,8}*1760, {22,2,20}*1760, {22,10,4}*1760, {110,2,4}*1760
   11-fold covers : {121,2,4}*1936, {11,2,44}*1936, {11,22,4}*1936
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)(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*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)!(13,14);
s3 := Sym(15)!(12,13)(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*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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