Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,16}

Atlas Canonical Name {2,4,16}*256a

Overview

Group
SmallGroup(256,26498)
Rank
4
Schläfli Type
{2,4,16}
Vertices, edges, …
2, 4, 32, 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

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