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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,22}*1408
if this polytope has a name.
Group : SmallGroup(1408,17945)
Rank : 5
Schlafli Type : {4,2,4,22}
Number of vertices, edges, etc : 4, 4, 4, 44, 22
Order of s₀s₁s₂s₃s₄ : 44
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,4,22}*704, {4,2,2,22}*704
   4-fold quotients : {4,2,2,11}*352, {2,2,2,22}*352
   8-fold quotients : {2,2,2,11}*176
   11-fold quotients : {4,2,4,2}*128
   22-fold quotients : {2,2,4,2}*64, {4,2,2,2}*64
   44-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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