Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,30}

Atlas Canonical Name {2,4,30}*480a

Overview

Group
SmallGroup(480,1169)
Rank
4
Schläfli Type
{2,4,30}
Vertices, edges, …
2, 4, 60, 30
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

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