Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,51,2}

Atlas Canonical Name {6,51,2}*1632

Overview

Group
SmallGroup(1632,1195)
Rank
4
Schläfli Type
{6,51,2}
Vertices, edges, …
8, 204, 68, 2
Order of s0s1s2s3
68
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

17-fold

34-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)(54,55)(58,59)(62,63)(66,67);;
s1 := ( 3, 4)( 5,65)( 6,66)( 7,68)( 8,67)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,53)(18,54)(19,56)(20,55)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)(32,43)(33,37)(34,38)(35,40)(36,39);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,68)(10,66)(11,67)(12,65)(13,64)(14,62)(15,63)(16,61)(17,60)(18,58)(19,59)(20,57)(21,56)(22,54)(23,55)(24,53)(25,52)(26,50)(27,51)(28,49)(29,48)(30,46)(31,47)(32,45)(33,44)(34,42)(35,43)(36,41)(37,40);;
s3 := (69,70);;
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*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(70)!( 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)(54,55)(58,59)(62,63)(66,67);
s1 := Sym(70)!( 3, 4)( 5,65)( 6,66)( 7,68)( 8,67)( 9,61)(10,62)(11,64)(12,63)(13,57)(14,58)(15,60)(16,59)(17,53)(18,54)(19,56)(20,55)(21,49)(22,50)(23,52)(24,51)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)(32,43)(33,37)(34,38)(35,40)(36,39);
s2 := Sym(70)!( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,68)(10,66)(11,67)(12,65)(13,64)(14,62)(15,63)(16,61)(17,60)(18,58)(19,59)(20,57)(21,56)(22,54)(23,55)(24,53)(25,52)(26,50)(27,51)(28,49)(29,48)(30,46)(31,47)(32,45)(33,44)(34,42)(35,43)(36,41)(37,40);
s3 := Sym(70)!(69,70);
poly := sub<Sym(70)|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*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2 >;