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

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