Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,39,2}

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

Overview

Group
SmallGroup(1248,1438)
Rank
4
Schläfli Type
{6,39,2}
Vertices, edges, …
8, 156, 52, 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)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51);;
s1 := ( 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);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,52)(10,50)(11,51)(12,49)(13,48)(14,46)(15,47)(16,45)(17,44)(18,42)(19,43)(20,41)(21,40)(22,38)(23,39)(24,37)(25,36)(26,34)(27,35)(28,33)(29,32);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(54)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51);
s1 := 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);
s2 := Sym(54)!( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,52)(10,50)(11,51)(12,49)(13,48)(14,46)(15,47)(16,45)(17,44)(18,42)(19,43)(20,41)(21,40)(22,38)(23,39)(24,37)(25,36)(26,34)(27,35)(28,33)(29,32);
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;