Polytope of Type {2,52,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,52,6}*1248b
if this polytope has a name.
Group : SmallGroup(1248,1438)
Rank : 4
Schlafli Type : {2,52,6}
Number of vertices, edges, etc : 2, 52, 156, 6
Order of s₀s₁s₂s₃ : 78
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   13-fold quotients : {2,4,6}*96b
   26-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

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