Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,16}

Atlas Canonical Name {2,8,16}*512b

Overview

Group
SmallGroup(512,396070)
Rank
4
Schläfli Type
{2,8,16}
Vertices, edges, …
2, 8, 64, 16
Order of s0s1s2s3
16
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

32-fold

Covers minimal covers in bold

None in this atlas.

Representations

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