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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,26}*1248
if this polytope has a name.
Group : SmallGroup(1248,1329)
Rank : 5
Schlafli Type : {3,2,4,26}
Number of vertices, edges, etc : 3, 3, 4, 52, 26
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 : {3,2,2,26}*624
   4-fold quotients : {3,2,2,13}*312
   13-fold quotients : {3,2,4,2}*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 := (30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)
(40,53)(41,54)(42,55);;
s3 := ( 4,30)( 5,42)( 6,41)( 7,40)( 8,39)( 9,38)(10,37)(11,36)(12,35)(13,34)
(14,33)(15,32)(16,31)(17,43)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)
(25,48)(26,47)(27,46)(28,45)(29,44);;
s4 := ( 4, 5)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(17,18)(19,29)(20,28)(21,27)
(22,26)(23,25)(30,31)(32,42)(33,41)(34,40)(35,39)(36,38)(43,44)(45,55)(46,54)
(47,53)(48,52)(49,51);;
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*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*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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