Part of the Atlas of Small Regular Polytopes

Polytope of Type {51,6,2}

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

Overview

Group
SmallGroup(1632,1195)
Rank
4
Schläfli Type
{51,6,2}
Vertices, edges, …
68, 204, 8, 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)( 5,65)( 6,67)( 7,66)( 8,68)( 9,61)(10,63)(11,62)(12,64)(13,57)(14,59)(15,58)(16,60)(17,53)(18,55)(19,54)(20,56)(21,49)(22,51)(23,50)(24,52)(25,45)(26,47)(27,46)(28,48)(29,41)(30,43)(31,42)(32,44)(33,37)(34,39)(35,38)(36,40);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,65)(10,66)(11,68)(12,67)(13,61)(14,62)(15,64)(16,63)(17,57)(18,58)(19,60)(20,59)(21,53)(22,54)(23,56)(24,55)(25,49)(26,50)(27,52)(28,51)(29,45)(30,46)(31,48)(32,47)(33,41)(34,42)(35,44)(36,43)(39,40);;
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)(53,56)(57,60)(61,64)(65,68);;
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*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(70)!( 2, 3)( 5,65)( 6,67)( 7,66)( 8,68)( 9,61)(10,63)(11,62)(12,64)(13,57)(14,59)(15,58)(16,60)(17,53)(18,55)(19,54)(20,56)(21,49)(22,51)(23,50)(24,52)(25,45)(26,47)(27,46)(28,48)(29,41)(30,43)(31,42)(32,44)(33,37)(34,39)(35,38)(36,40);
s1 := Sym(70)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 9,65)(10,66)(11,68)(12,67)(13,61)(14,62)(15,64)(16,63)(17,57)(18,58)(19,60)(20,59)(21,53)(22,54)(23,56)(24,55)(25,49)(26,50)(27,52)(28,51)(29,45)(30,46)(31,48)(32,47)(33,41)(34,42)(35,44)(36,43)(39,40);
s2 := Sym(70)!( 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)(53,56)(57,60)(61,64)(65,68);
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*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*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;