Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,8,2}

Atlas Canonical Name {8,8,2}*256d

Overview

Group
SmallGroup(256,11966)
Rank
4
Schläfli Type
{8,8,2}
Vertices, edges, …
8, 32, 8, 2
Order of s0s1s2s3
8
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

8-fold

16-fold

Covers minimal covers in bold

2-fold

3-fold

5-fold

7-fold

Representations

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