Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,15,6}

Atlas Canonical Name {2,15,6}*360

Overview

Group
SmallGroup(360,154)
Rank
4
Schläfli Type
{2,15,6}
Vertices, edges, …
2, 15, 45, 6
Order of s0s1s2s3
30
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

5-fold

9-fold

15-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

Representations

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