Polytope of Type {4,39,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,39,2,3}*1872
if this polytope has a name.
Group : SmallGroup(1872,1036)
Rank : 5
Schlafli Type : {4,39,2,3}
Number of vertices, edges, etc : 4, 78, 39, 3, 3
Order of s₀s₁s₂s₃s₄ : 39
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {4,3,2,3}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 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);;
s1 := ( 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);;
s2 := ( 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);;
s3 := (54,55);;
s4 := (53,54);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(55)!( 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);
s1 := Sym(55)!( 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);
s2 := Sym(55)!( 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);
s3 := Sym(55)!(54,55);
s4 := Sym(55)!(53,54);
poly := sub<Sym(55)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope