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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,22,4}*1408
if this polytope has a name.
Group : SmallGroup(1408,19301)
Rank : 6
Schlafli Type : {2,2,2,22,4}
Number of vertices, edges, etc : 2, 2, 2, 22, 44, 4
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 : {2,2,2,22,2}*704
   4-fold quotients : {2,2,2,11,2}*352
   11-fold quotients : {2,2,2,2,4}*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 := ( 8,17)( 9,16)(10,15)(11,14)(12,13)(19,28)(20,27)(21,26)(22,25)(23,24)
(30,39)(31,38)(32,37)(33,36)(34,35)(41,50)(42,49)(43,48)(44,47)(45,46);;
s4 := ( 7, 8)( 9,17)(10,16)(11,15)(12,14)(18,19)(20,28)(21,27)(22,26)(23,25)
(29,41)(30,40)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)
(39,42);;
s5 := ( 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)(25,47)(26,48)(27,49)
(28,50);;
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*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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