Polytope of Type {39,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39,6}*624
if this polytope has a name.
Group : SmallGroup(624,242)
Rank : 3
Schlafli Type : {39,6}
Number of vertices, edges, etc : 52, 156, 8
Order of s₀s₁s₂ : 52
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {39,6,2} of size 1248
Vertex Figure Of :
   {2,39,6} of size 1248
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {13,2}*52
   13-fold quotients : {3,6}*48
   26-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {39,12}*1248, {78,6}*1248
   3-fold covers : {39,6}*1872
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope