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

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

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