Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,39}

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

Overview

Group
SmallGroup(1248,1438)
Rank
4
Schläfli Type
{2,6,39}
Vertices, edges, …
2, 8, 156, 52
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 := (1,2);;
s1 := ( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45)(48,49)(52,53);;
s2 := ( 5, 6)( 7,51)( 8,52)( 9,54)(10,53)(11,47)(12,48)(13,50)(14,49)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,35)(24,36)(25,38)(26,37)(27,31)(28,32)(29,34)(30,33);;
s3 := ( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,54)(12,52)(13,53)(14,51)(15,50)(16,48)(17,49)(18,47)(19,46)(20,44)(21,45)(22,43)(23,42)(24,40)(25,41)(26,39)(27,38)(28,36)(29,37)(30,35)(31,34);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(54)!(1,2);
s1 := Sym(54)!( 4, 5)( 8, 9)(12,13)(16,17)(20,21)(24,25)(28,29)(32,33)(36,37)(40,41)(44,45)(48,49)(52,53);
s2 := Sym(54)!( 5, 6)( 7,51)( 8,52)( 9,54)(10,53)(11,47)(12,48)(13,50)(14,49)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,35)(24,36)(25,38)(26,37)(27,31)(28,32)(29,34)(30,33);
s3 := Sym(54)!( 3,10)( 4, 8)( 5, 9)( 6, 7)(11,54)(12,52)(13,53)(14,51)(15,50)(16,48)(17,49)(18,47)(19,46)(20,44)(21,45)(22,43)(23,42)(24,40)(25,41)(26,39)(27,38)(28,36)(29,37)(30,35)(31,34);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3 >;