Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,8}

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

Overview

Group
SmallGroup(256,11966)
Rank
4
Schläfli Type
{2,8,8}
Vertices, edges, …
2, 8, 32, 8
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 := (1,2);;
s1 := ( 3,19)( 4,20)( 5,21)( 6,22)( 7,26)( 8,25)( 9,24)(10,23)(11,28)(12,27)(13,30)(14,29)(15,33)(16,34)(17,31)(18,32)(35,51)(36,52)(37,53)(38,54)(39,58)(40,57)(41,56)(42,55)(43,60)(44,59)(45,62)(46,61)(47,65)(48,66)(49,63)(50,64);;
s2 := ( 7,10)( 8, 9)(11,13)(12,14)(15,16)(17,18)(19,23)(20,24)(21,25)(22,26)(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,50)(40,49)(41,48)(42,47)(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);;
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, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 3,19)( 4,20)( 5,21)( 6,22)( 7,26)( 8,25)( 9,24)(10,23)(11,28)(12,27)(13,30)(14,29)(15,33)(16,34)(17,31)(18,32)(35,51)(36,52)(37,53)(38,54)(39,58)(40,57)(41,56)(42,55)(43,60)(44,59)(45,62)(46,61)(47,65)(48,66)(49,63)(50,64);
s2 := Sym(66)!( 7,10)( 8, 9)(11,13)(12,14)(15,16)(17,18)(19,23)(20,24)(21,25)(22,26)(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,50)(40,49)(41,48)(42,47)(51,64)(52,63)(53,66)(54,65)(55,60)(56,59)(57,62)(58,61);
s3 := Sym(66)!( 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);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2 >;