Part of the Atlas of Small Regular Polytopes

Polytope of Type {39,6,2}

Atlas Canonical Name {39,6,2}*1248

Overview

Group
SmallGroup(1248,1438)
Rank
4
Schläfli Type
{39,6,2}
Vertices, edges, …
52, 156, 8, 2
Order of s0s1s2s3
52
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

12-fold

13-fold

26-fold

Covers minimal covers in bold

None in this atlas.

Representations

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);;
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, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*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)!( 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(54)!( 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(54)!( 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);
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, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*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, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;