Polytope of Type {22,4,2}

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

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

to this polytope