Polytope of Type {2,22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,4}*352
if this polytope has a name.
Group : SmallGroup(352,177)
Rank : 4
Schlafli Type : {2,22,4}
Number of vertices, edges, etc : 2, 22, 44, 4
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,22,4,2} of size 704
   {2,22,4,4} of size 1408
Vertex Figure Of :
   {2,2,22,4} of size 704
   {3,2,22,4} of size 1056
   {4,2,22,4} of size 1408
   {5,2,22,4} of size 1760
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,22,2}*176
   4-fold quotients : {2,11,2}*88
   11-fold quotients : {2,2,4}*32
   22-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,44,4}*704, {4,22,4}*704, {2,22,8}*704
   3-fold covers : {2,22,12}*1056, {6,22,4}*1056, {2,66,4}*1056a
   4-fold covers : {4,44,4}*1408, {2,44,8}*1408a, {2,88,4}*1408a, {2,44,8}*1408b, {2,88,4}*1408b, {2,44,4}*1408, {4,22,8}*1408, {8,22,4}*1408, {2,22,16}*1408
   5-fold covers : {2,22,20}*1760, {10,22,4}*1760, {2,110,4}*1760
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(15,24)(16,23)(17,22)(18,21)(19,20)
(26,35)(27,34)(28,33)(29,32)(30,31)(37,46)(38,45)(39,44)(40,43)(41,42);;
s2 := ( 3, 4)( 5,13)( 6,12)( 7,11)( 8,10)(14,15)(16,24)(17,23)(18,22)(19,21)
(25,37)(26,36)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)
(35,38);;
s3 := ( 3,25)( 4,26)( 5,27)( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)(12,34)
(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)
(24,46);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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(46)!(1,2);
s1 := Sym(46)!( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(15,24)(16,23)(17,22)(18,21)
(19,20)(26,35)(27,34)(28,33)(29,32)(30,31)(37,46)(38,45)(39,44)(40,43)(41,42);
s2 := Sym(46)!( 3, 4)( 5,13)( 6,12)( 7,11)( 8,10)(14,15)(16,24)(17,23)(18,22)
(19,21)(25,37)(26,36)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)
(35,38);
s3 := Sym(46)!( 3,25)( 4,26)( 5,27)( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)
(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)
(23,45)(24,46);
poly := sub<Sym(46)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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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