Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,60,6}

Atlas Canonical Name {2,60,6}*1440d

Overview

Group
SmallGroup(1440,5901)
Rank
4
Schläfli Type
{2,60,6}
Vertices, edges, …
2, 60, 180, 6
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

15-fold

30-fold

Covers minimal covers in bold

None in this atlas.

Representations

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