Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(512,6255213)
Rank
5
Schläfli Type
{2,2,8,8}
Vertices, edges, …
2, 2, 8, 32, 8
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 := (3,4);;
s2 := ( 5,37)( 6,38)( 7,39)( 8,40)( 9,42)(10,41)(11,44)(12,43)(13,47)(14,48)(15,45)(16,46)(17,52)(18,51)(19,50)(20,49)(21,53)(22,54)(23,55)(24,56)(25,58)(26,57)(27,60)(28,59)(29,63)(30,64)(31,61)(32,62)(33,68)(34,67)(35,66)(36,65);;
s3 := ( 9,10)(11,12)(13,15)(14,16)(17,20)(18,19)(21,25)(22,26)(23,27)(24,28)(29,35)(30,36)(31,33)(32,34)(37,45)(38,46)(39,47)(40,48)(41,50)(42,49)(43,52)(44,51)(53,66)(54,65)(55,68)(56,67)(57,62)(58,61)(59,64)(60,63);;
s4 := ( 5,21)( 6,22)( 7,23)( 8,24)( 9,26)(10,25)(11,28)(12,27)(13,30)(14,29)(15,32)(16,31)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,64)(48,63)(49,65)(50,66)(51,67)(52,68);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(68)!(1,2);
s1 := Sym(68)!(3,4);
s2 := Sym(68)!( 5,37)( 6,38)( 7,39)( 8,40)( 9,42)(10,41)(11,44)(12,43)(13,47)(14,48)(15,45)(16,46)(17,52)(18,51)(19,50)(20,49)(21,53)(22,54)(23,55)(24,56)(25,58)(26,57)(27,60)(28,59)(29,63)(30,64)(31,61)(32,62)(33,68)(34,67)(35,66)(36,65);
s3 := Sym(68)!( 9,10)(11,12)(13,15)(14,16)(17,20)(18,19)(21,25)(22,26)(23,27)(24,28)(29,35)(30,36)(31,33)(32,34)(37,45)(38,46)(39,47)(40,48)(41,50)(42,49)(43,52)(44,51)(53,66)(54,65)(55,68)(56,67)(57,62)(58,61)(59,64)(60,63);
s4 := Sym(68)!( 5,21)( 6,22)( 7,23)( 8,24)( 9,26)(10,25)(11,28)(12,27)(13,30)(14,29)(15,32)(16,31)(17,33)(18,34)(19,35)(20,36)(37,53)(38,54)(39,55)(40,56)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,64)(48,63)(49,65)(50,66)(51,67)(52,68);
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3 >;