Part of the Atlas of Small Regular Polytopes

Polytope of Type {64,2}

Atlas Canonical Name {64,2}*256

Overview

Group
SmallGroup(256,6726)
Rank
3
Schläfli Type
{64,2}
Vertices, edges, …
64, 64, 2
Order of s0s1s2
64
Order of s0s1s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

32-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

7-fold

Representations

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