Polytope of Type {3,2,26,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,26,4}*1248
if this polytope has a name.
Group : SmallGroup(1248,1329)
Rank : 5
Schlafli Type : {3,2,26,4}
Number of vertices, edges, etc : 3, 3, 26, 52, 4
Order of s₀s₁s₂s₃s₄ : 156
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 : {3,2,26,2}*624
   4-fold quotients : {3,2,13,2}*312
   13-fold quotients : {3,2,2,4}*96
   26-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(18,29)(19,28)(20,27)(21,26)
(22,25)(23,24)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(44,55)(45,54)(46,53)
(47,52)(48,51)(49,50);;
s3 := ( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,18)(19,29)(20,28)(21,27)
(22,26)(23,25)(30,44)(31,43)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)
(39,48)(40,47)(41,46)(42,45);;
s4 := ( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)(13,39)
(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)(24,50)
(25,51)(26,52)(27,53)(28,54)(29,55);;
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, 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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(55)!(2,3);
s1 := Sym(55)!(1,2);
s2 := Sym(55)!( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(18,29)(19,28)(20,27)
(21,26)(22,25)(23,24)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(44,55)(45,54)
(46,53)(47,52)(48,51)(49,50);
s3 := Sym(55)!( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,18)(19,29)(20,28)
(21,27)(22,26)(23,25)(30,44)(31,43)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)
(38,49)(39,48)(40,47)(41,46)(42,45);
s4 := Sym(55)!( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)(10,36)(11,37)(12,38)
(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)(22,48)(23,49)
(24,50)(25,51)(26,52)(27,53)(28,54)(29,55);
poly := sub<Sym(55)|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, 
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*s2*s3*s2*s3*s2*s3*s2*s3 >;

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