Polytope of Type {39,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39,4,2}*624
if this polytope has a name.
Group : SmallGroup(624,245)
Rank : 4
Schlafli Type : {39,4,2}
Number of vertices, edges, etc : 39, 78, 4, 2
Order of s₀s₁s₂s₃ : 78
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {39,4,2,2} of size 1248
   {39,4,2,3} of size 1872
Vertex Figure Of :
   {2,39,4,2} of size 1248
Quotients (Maximal Quotients in Boldface) :
   13-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {39,4,2}*1248, {78,4,2}*1248b, {78,4,2}*1248c
   3-fold covers : {117,4,2}*1872
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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