Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,15,6}*720

Overview

Group
SmallGroup(720,831)
Rank
5
Schläfli Type
{2,2,15,6}
Vertices, edges, …
2, 2, 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

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)(34,41);;
s3 := ( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)(14,22)(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49);;
s4 := (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)(34,49);;
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*s1*s0*s1, 
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, 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(49)!(1,2);
s1 := Sym(49)!(3,4);
s2 := Sym(49)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)(34,41);
s3 := Sym(49)!( 5,26)( 6,25)( 7,29)( 8,28)( 9,27)(10,21)(11,20)(12,24)(13,23)(14,22)(15,31)(16,30)(17,34)(18,33)(19,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49);
s4 := Sym(49)!(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)(34,49);
poly := sub<Sym(49)|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*s1*s0*s1, 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, 
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 >;