Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,20,2}

Atlas Canonical Name {6,20,2}*480a

Overview

Group
SmallGroup(480,1088)
Rank
4
Schläfli Type
{6,20,2}
Vertices, edges, …
6, 60, 20, 2
Order of s0s1s2s3
60
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

3-fold

5-fold

6-fold

10-fold

12-fold

15-fold

20-fold

30-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

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