Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1248,1441)
Rank
5
Schläfli Type
{2,2,39,4}
Vertices, edges, …
2, 2, 39, 78, 4
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 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,53)(10,54)(11,56)(12,55)(13,49)(14,50)(15,52)(16,51)(17,45)(18,46)(19,48)(20,47)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,33)(30,34)(31,36)(32,35);;
s3 := ( 5, 9)( 6,11)( 7,10)( 8,12)(13,53)(14,55)(15,54)(16,56)(17,49)(18,51)(19,50)(20,52)(21,45)(22,47)(23,46)(24,48)(25,41)(26,43)(27,42)(28,44)(29,37)(30,39)(31,38)(32,40)(34,35);;
s4 := ( 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)(53,54)(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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(56)!(1,2);
s1 := Sym(56)!(3,4);
s2 := Sym(56)!( 7, 8)( 9,53)(10,54)(11,56)(12,55)(13,49)(14,50)(15,52)(16,51)(17,45)(18,46)(19,48)(20,47)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,33)(30,34)(31,36)(32,35);
s3 := Sym(56)!( 5, 9)( 6,11)( 7,10)( 8,12)(13,53)(14,55)(15,54)(16,56)(17,49)(18,51)(19,50)(20,52)(21,45)(22,47)(23,46)(24,48)(25,41)(26,43)(27,42)(28,44)(29,37)(30,39)(31,38)(32,40)(34,35);
s4 := Sym(56)!( 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)(53,54)(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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;