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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,2,2}*352
if this polytope has a name.
Group : SmallGroup(352,194)
Rank : 5
Schlafli Type : {2,22,2,2}
Number of vertices, edges, etc : 2, 22, 22, 2, 2
Order of s0s1s2s3s4 : 22
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,22,2,2,2} of size 704
   {2,22,2,2,3} of size 1056
   {2,22,2,2,4} of size 1408
   {2,22,2,2,5} of size 1760
Vertex Figure Of :
   {2,2,22,2,2} of size 704
   {3,2,22,2,2} of size 1056
   {4,2,22,2,2} of size 1408
   {5,2,22,2,2} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,11,2,2}*176
   11-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,44,2,2}*704, {2,22,2,4}*704, {2,22,4,2}*704, {4,22,2,2}*704
   3-fold covers : {2,22,2,6}*1056, {2,22,6,2}*1056, {6,22,2,2}*1056, {2,66,2,2}*1056
   4-fold covers : {2,22,4,4}*1408, {2,44,4,2}*1408, {4,44,2,2}*1408, {4,22,2,4}*1408, {4,22,4,2}*1408, {2,44,2,4}*1408, {2,22,2,8}*1408, {2,22,8,2}*1408, {8,22,2,2}*1408, {2,88,2,2}*1408
   5-fold covers : {2,22,2,10}*1760, {2,22,10,2}*1760, {10,22,2,2}*1760, {2,110,2,2}*1760
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,24);;
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*s1*s0*s1, 
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(28)!(1,2);
s1 := Sym(28)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24);
s2 := Sym(28)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,24);
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*s1*s0*s1, s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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