Polytope of Type {2,4,22}

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

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

Permutation Representation (Magma) :

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

to this polytope