Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,15,6}

Atlas Canonical Name {3,2,15,6}*1080

Overview

Group
SmallGroup(1080,539)
Rank
5
Schläfli Type
{3,2,15,6}
Vertices, edges, …
3, 3, 15, 45, 6
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

9-fold

15-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)( 9,14)(10,18)(11,17)(12,16)(13,15)(19,34)(20,38)(21,37)(22,36)(23,35)(24,44)(25,48)(26,47)(27,46)(28,45)(29,39)(30,43)(31,42)(32,41)(33,40);;
s3 := ( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,20)(10,19)(11,23)(12,22)(13,21)(14,30)(15,29)(16,33)(17,32)(18,31)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48);;
s4 := (19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(33,48);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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(48)!(2,3);
s1 := Sym(48)!(1,2);
s2 := Sym(48)!( 5, 8)( 6, 7)( 9,14)(10,18)(11,17)(12,16)(13,15)(19,34)(20,38)(21,37)(22,36)(23,35)(24,44)(25,48)(26,47)(27,46)(28,45)(29,39)(30,43)(31,42)(32,41)(33,40);
s3 := Sym(48)!( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,20)(10,19)(11,23)(12,22)(13,21)(14,30)(15,29)(16,33)(17,32)(18,31)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48);
s4 := Sym(48)!(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(33,48);
poly := sub<Sym(48)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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 >;