Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,6,16}

Atlas Canonical Name {2,2,6,16}*768

Overview

Group
SmallGroup(768,1076041)
Rank
5
Schläfli Type
{2,2,6,16}
Vertices, edges, …
2, 2, 6, 48, 16
Order of s0s1s2s3s4
48
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

3-fold

4-fold

6-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52);;
s3 := ( 5, 6)( 8, 9)(11,15)(12,14)(13,16)(17,24)(18,23)(19,25)(20,27)(21,26)(22,28)(29,48)(30,47)(31,49)(32,51)(33,50)(34,52)(35,42)(36,41)(37,43)(38,45)(39,44)(40,46);;
s4 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,35)(15,36)(16,37)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,41)(24,42)(25,43)(26,44)(27,45)(28,46);;
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, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52);
s3 := Sym(52)!( 5, 6)( 8, 9)(11,15)(12,14)(13,16)(17,24)(18,23)(19,25)(20,27)(21,26)(22,28)(29,48)(30,47)(31,49)(32,51)(33,50)(34,52)(35,42)(36,41)(37,43)(38,45)(39,44)(40,46);
s4 := Sym(52)!( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,35)(15,36)(16,37)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,41)(24,42)(25,43)(26,44)(27,45)(28,46);
poly := sub<Sym(52)|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, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;