Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,60,2}

Atlas Canonical Name {2,60,2}*480

Overview

Group
SmallGroup(480,1167)
Rank
4
Schläfli Type
{2,60,2}
Vertices, edges, …
2, 60, 60, 2
Order of s0s1s2s3
60
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat
  • Self-Dual

Quotients maximal quotients in bold

2-fold

3-fold

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