Polytope of Type {4,22,2}

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

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

to this polytope