Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,64,2}

Atlas Canonical Name {2,64,2}*512

Overview

Group
SmallGroup(512,420505)
Rank
4
Schläfli Type
{2,64,2}
Vertices, edges, …
2, 64, 64, 2
Order of s0s1s2s3
64
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat
  • Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

Covers minimal covers in bold

None in this atlas.

Representations

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