Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1080,539)
Rank
5
Schläfli Type
{3,2,6,15}
Vertices, edges, …
3, 3, 6, 45, 15
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 := (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);;
s3 := ( 4,19)( 5,23)( 6,22)( 7,21)( 8,20)( 9,29)(10,33)(11,32)(12,31)(13,30)(14,24)(15,28)(16,27)(17,26)(18,25)(35,38)(36,37)(39,44)(40,48)(41,47)(42,46)(43,45);;
s4 := ( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,40)(20,39)(21,43)(22,42)(23,41)(24,35)(25,34)(26,38)(27,37)(28,36)(29,45)(30,44)(31,48)(32,47)(33,46);;
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, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!(2,3);
s1 := Sym(48)!(1,2);
s2 := 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);
s3 := Sym(48)!( 4,19)( 5,23)( 6,22)( 7,21)( 8,20)( 9,29)(10,33)(11,32)(12,31)(13,30)(14,24)(15,28)(16,27)(17,26)(18,25)(35,38)(36,37)(39,44)(40,48)(41,47)(42,46)(43,45);
s4 := Sym(48)!( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,40)(20,39)(21,43)(22,42)(23,41)(24,35)(25,34)(26,38)(27,37)(28,36)(29,45)(30,44)(31,48)(32,47)(33,46);
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, 
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;