Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,34,2}

Atlas Canonical Name {4,34,2}*544

Overview

Group
SmallGroup(544,225)
Rank
4
Schläfli Type
{4,34,2}
Vertices, edges, …
4, 68, 34, 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

2-fold

4-fold

17-fold

34-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

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