Polytope of Type {2,39,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,39,6}*1248
if this polytope has a name.
Group : SmallGroup(1248,1438)
Rank : 4
Schlafli Type : {2,39,6}
Number of vertices, edges, etc : 2, 52, 156, 8
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   12-fold quotients : {2,13,2}*104
   13-fold quotients : {2,3,6}*96
   26-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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