Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,15,2}

Atlas Canonical Name {3,2,4,15,2}*1440

Overview

Group
SmallGroup(1440,5900)
Rank
6
Schläfli Type
{3,2,4,15,2}
Vertices, edges, …
3, 3, 4, 30, 15, 2
Order of s0s1s2s3s4s5
30
Order of s0s1s2s3s4s5s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 7)( 5, 9)( 6,11)( 8,14)(10,18)(12,13)(15,19)(16,17)(20,23)(21,22);;
s3 := ( 5, 6)( 7,12)( 8,10)( 9,15)(11,16)(14,20)(17,19)(18,21)(22,23);;
s4 := ( 4, 5)( 6, 8)( 7, 9)(11,14)(12,17)(13,16)(15,22)(19,21)(20,23);;
s5 := (24,25);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, 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(25)!(2,3);
s1 := Sym(25)!(1,2);
s2 := Sym(25)!( 4, 7)( 5, 9)( 6,11)( 8,14)(10,18)(12,13)(15,19)(16,17)(20,23)(21,22);
s3 := Sym(25)!( 5, 6)( 7,12)( 8,10)( 9,15)(11,16)(14,20)(17,19)(18,21)(22,23);
s4 := Sym(25)!( 4, 5)( 6, 8)( 7, 9)(11,14)(12,17)(13,16)(15,22)(19,21)(20,23);
s5 := Sym(25)!(24,25);
poly := sub<Sym(25)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, 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 >;