Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {39,4,2,2}*1248

Overview

Group
SmallGroup(1248,1441)
Rank
5
Schläfli Type
{39,4,2,2}
Vertices, edges, …
39, 78, 4, 2, 2
Order of s0s1s2s3s4
78
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

13-fold

Covers minimal covers in bold

None in this atlas.

Representations

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);;
s4 := (55,56);;
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, 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(56)!( 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(56)!( 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(56)!( 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(56)!(53,54);
s4 := Sym(56)!(55,56);
poly := sub<Sym(56)|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, 
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 >;