Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,8,2}

Atlas Canonical Name {2,8,8,2}*512a

Overview

Group
SmallGroup(512,6255213)
Rank
5
Schläfli Type
{2,8,8,2}
Vertices, edges, …
2, 8, 32, 8, 2
Order of s0s1s2s3s4
8
Order of s0s1s2s3s4s3s2s1
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

8-fold

16-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 3,19)( 4,20)( 5,21)( 6,22)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,30)(14,29)(15,31)(16,32)(17,33)(18,34)(35,51)(36,52)(37,53)(38,54)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64)(49,65)(50,66);;
s2 := ( 7, 8)( 9,10)(11,13)(12,14)(15,18)(16,17)(19,23)(20,24)(21,25)(22,26)(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,48)(40,47)(41,50)(42,49)(51,64)(52,63)(53,66)(54,65)(55,60)(56,59)(57,62)(58,61);;
s3 := ( 3,35)( 4,36)( 5,37)( 6,38)( 7,40)( 8,39)( 9,42)(10,41)(11,45)(12,46)(13,43)(14,44)(15,50)(16,49)(17,48)(18,47)(19,51)(20,52)(21,53)(22,54)(23,56)(24,55)(25,58)(26,57)(27,61)(28,62)(29,59)(30,60)(31,66)(32,65)(33,64)(34,63);;
s4 := (67,68);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(68)!(1,2);
s1 := Sym(68)!( 3,19)( 4,20)( 5,21)( 6,22)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,30)(14,29)(15,31)(16,32)(17,33)(18,34)(35,51)(36,52)(37,53)(38,54)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64)(49,65)(50,66);
s2 := Sym(68)!( 7, 8)( 9,10)(11,13)(12,14)(15,18)(16,17)(19,23)(20,24)(21,25)(22,26)(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,48)(40,47)(41,50)(42,49)(51,64)(52,63)(53,66)(54,65)(55,60)(56,59)(57,62)(58,61);
s3 := Sym(68)!( 3,35)( 4,36)( 5,37)( 6,38)( 7,40)( 8,39)( 9,42)(10,41)(11,45)(12,46)(13,43)(14,44)(15,50)(16,49)(17,48)(18,47)(19,51)(20,52)(21,53)(22,54)(23,56)(24,55)(25,58)(26,57)(27,61)(28,62)(29,59)(30,60)(31,66)(32,65)(33,64)(34,63);
s4 := Sym(68)!(67,68);
poly := sub<Sym(68)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;