Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,20,6}

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

Overview

Group
SmallGroup(480,1088)
Rank
4
Schläfli Type
{2,20,6}
Vertices, edges, …
2, 20, 60, 6
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 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)(41,55)(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);;
s2 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)(12,45)(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)(23,59)(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);;
s3 := ( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)(22,27)(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);;
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*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)!(1,2);
s1 := Sym(62)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,53)(39,57)(40,56)(41,55)(42,54)(43,58)(44,62)(45,61)(46,60)(47,59);
s2 := Sym(62)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,44)( 9,43)(10,47)(11,46)(12,45)(13,39)(14,38)(15,42)(16,41)(17,40)(18,49)(19,48)(20,52)(21,51)(22,50)(23,59)(24,58)(25,62)(26,61)(27,60)(28,54)(29,53)(30,57)(31,56)(32,55);
s3 := Sym(62)!( 3, 8)( 4, 9)( 5,10)( 6,11)( 7,12)(18,23)(19,24)(20,25)(21,26)(22,27)(33,38)(34,39)(35,40)(36,41)(37,42)(48,53)(49,54)(50,55)(51,56)(52,57);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;