Polytope of Type {2,2,22,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,22,2}*352
if this polytope has a name.
Group : SmallGroup(352,194)
Rank : 5
Schlafli Type : {2,2,22,2}
Number of vertices, edges, etc : 2, 2, 22, 22, 2
Order of s₀s₁s₂s₃s₄ : 22
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,22,2,2} of size 704
   {2,2,22,2,3} of size 1056
   {2,2,22,2,4} of size 1408
   {2,2,22,2,5} of size 1760
Vertex Figure Of :
   {2,2,2,22,2} of size 704
   {3,2,2,22,2} of size 1056
   {4,2,2,22,2} of size 1408
   {5,2,2,22,2} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,11,2}*176
   11-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,44,2}*704, {2,2,22,4}*704, {2,4,22,2}*704, {4,2,22,2}*704
   3-fold covers : {2,2,22,6}*1056, {2,6,22,2}*1056, {6,2,22,2}*1056, {2,2,66,2}*1056
   4-fold covers : {4,4,22,2}*1408, {2,2,44,4}*1408, {2,4,44,2}*1408, {4,2,22,4}*1408, {2,4,22,4}*1408, {4,2,44,2}*1408, {2,2,22,8}*1408, {2,8,22,2}*1408, {8,2,22,2}*1408, {2,2,88,2}*1408
   5-fold covers : {2,2,22,10}*1760, {2,10,22,2}*1760, {10,2,22,2}*1760, {2,2,110,2}*1760
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)
(24,26);;
s4 := (27,28);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(28)!(1,2);
s1 := Sym(28)!(3,4);
s2 := Sym(28)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26);
s3 := Sym(28)!( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)
(22,23)(24,26);
s4 := Sym(28)!(27,28);
poly := sub<Sym(28)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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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