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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,22,4}*1408
if this polytope has a name.
Group : SmallGroup(1408,17945)
Rank : 5
Schlafli Type : {4,2,22,4}
Number of vertices, edges, etc : 4, 4, 22, 44, 4
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 : {2,2,22,4}*704, {4,2,22,2}*704
   4-fold quotients : {4,2,11,2}*352, {2,2,22,2}*352
   8-fold quotients : {2,2,11,2}*176
   11-fold quotients : {4,2,2,4}*128
   22-fold quotients : {2,2,2,4}*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 := ( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)
(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44);;
s3 := ( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)(21,23)
(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)
(37,40);;
s4 := ( 5,27)( 6,28)( 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);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(48)!(2,3);
s1 := Sym(48)!(1,2)(3,4);
s2 := Sym(48)!( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)
(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44);
s3 := Sym(48)!( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)
(21,23)(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)
(37,40);
s4 := Sym(48)!( 5,27)( 6,28)( 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);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

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