Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,4,15}

Atlas Canonical Name {2,2,4,15}*480

Overview

Group
SmallGroup(480,1199)
Rank
5
Schläfli Type
{2,2,4,15}
Vertices, edges, …
2, 2, 4, 30, 15
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 8)( 6,10)( 7,12)( 9,15)(11,19)(13,14)(16,20)(17,18)(21,24)(22,23);;
s3 := ( 6, 7)( 8,13)( 9,11)(10,16)(12,17)(15,21)(18,20)(19,22)(23,24);;
s4 := ( 5, 6)( 7, 9)( 8,10)(12,15)(13,18)(14,17)(16,23)(20,22)(21,24);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*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(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!( 5, 8)( 6,10)( 7,12)( 9,15)(11,19)(13,14)(16,20)(17,18)(21,24)(22,23);
s3 := Sym(24)!( 6, 7)( 8,13)( 9,11)(10,16)(12,17)(15,21)(18,20)(19,22)(23,24);
s4 := Sym(24)!( 5, 6)( 7, 9)( 8,10)(12,15)(13,18)(14,17)(16,23)(20,22)(21,24);
poly := sub<Sym(24)|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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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 >;