Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,15}

Atlas Canonical Name {2,6,15}*1440e

Overview

Group
SmallGroup(1440,5901)
Rank
4
Schläfli Type
{2,6,15}
Vertices, edges, …
2, 24, 180, 60
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

3-fold

4-fold

5-fold

12-fold

15-fold

20-fold

30-fold

36-fold

60-fold

Covers minimal covers in bold

None in this atlas.

Representations

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