Polytope of Type {2,6,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,39}*1248
if this polytope has a name.
Group : SmallGroup(1248,1438)
Rank : 4
Schlafli Type : {2,6,39}
Number of vertices, edges, etc : 2, 8, 156, 52
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 : {2,2,13}*104
   13-fold quotients : {2,6,3}*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)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)
(44,45)(48,49)(52,53);;
s2 := ( 5, 6)( 7,51)( 8,52)( 9,54)(10,53)(11,47)(12,48)(13,50)(14,49)(15,43)
(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,35)(24,36)(25,38)(26,37)
(27,31)(28,32)(29,34)(30,33);;
s3 := ( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,54)(12,52)(13,53)(14,51)(15,50)(16,48)
(17,49)(18,47)(19,46)(20,44)(21,45)(22,43)(23,42)(24,40)(25,41)(26,39)(27,38)
(28,36)(29,37)(30,35)(31,34);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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