Part of the Atlas of Small Regular Polytopes

Polytope of Type {34,4,2}

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

Overview

Group
SmallGroup(544,225)
Rank
4
Schläfli Type
{34,4,2}
Vertices, edges, …
34, 68, 4, 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 := ( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61);;
s1 := ( 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)(35,53)(36,52)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54);;
s2 := ( 1,35)( 2,36)( 3,37)( 4,38)( 5,39)( 6,40)( 7,41)( 8,42)( 9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)(25,59)(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(70)!( 2,17)( 3,16)( 4,15)( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61);
s1 := 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)(35,53)(36,52)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54);
s2 := Sym(70)!( 1,35)( 2,36)( 3,37)( 4,38)( 5,39)( 6,40)( 7,41)( 8,42)( 9,43)(10,44)(11,45)(12,46)(13,47)(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)(25,59)(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;