Polytope of Type {2,2,2,4,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,22}*1408
if this polytope has a name.
Group : SmallGroup(1408,19301)
Rank : 6
Schlafli Type : {2,2,2,4,22}
Number of vertices, edges, etc : 2, 2, 2, 4, 44, 22
Order of s₀s₁s₂s₃s₄s₅ : 44
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,2,22}*704
   4-fold quotients : {2,2,2,2,11}*352
   11-fold quotients : {2,2,2,4,2}*128
   22-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)(36,47)(37,48)(38,49)
(39,50);;
s4 := ( 7,29)( 8,39)( 9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)
(17,30)(18,40)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)
(28,41);;
s5 := ( 7, 8)( 9,17)(10,16)(11,15)(12,14)(18,19)(20,28)(21,27)(22,26)(23,25)
(29,30)(31,39)(32,38)(33,37)(34,36)(40,41)(42,50)(43,49)(44,48)(45,47);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!(1,2);
s1 := Sym(50)!(3,4);
s2 := Sym(50)!(5,6);
s3 := Sym(50)!(29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)(36,47)(37,48)
(38,49)(39,50);
s4 := Sym(50)!( 7,29)( 8,39)( 9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)
(16,31)(17,30)(18,40)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)
(27,42)(28,41);
s5 := Sym(50)!( 7, 8)( 9,17)(10,16)(11,15)(12,14)(18,19)(20,28)(21,27)(22,26)
(23,25)(29,30)(31,39)(32,38)(33,37)(34,36)(40,41)(42,50)(43,49)(44,48)(45,47);
poly := sub<Sym(50)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope