Part of the Atlas of Small Regular Polytopes

Polytope of Type {5,2,30}

Atlas Canonical Name {5,2,30}*600

Overview

Group
SmallGroup(600,195)
Rank
4
Schläfli Type
{5,2,30}
Vertices, edges, …
5, 5, 30, 30
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

2-fold

3-fold

5-fold

6-fold

10-fold

15-fold

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP)
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(10,11)(12,13)(14,15)(16,19)(17,18)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,35)(33,34);;
s3 := ( 6,22)( 7,16)( 8,14)( 9,24)(10,12)(11,32)(13,18)(15,28)(17,26)(19,34)(20,23)(21,33)(25,30)(27,29)(31,35);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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*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(35)!(2,3)(4,5);
s1 := Sym(35)!(1,2)(3,4);
s2 := Sym(35)!( 8, 9)(10,11)(12,13)(14,15)(16,19)(17,18)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,35)(33,34);
s3 := Sym(35)!( 6,22)( 7,16)( 8,14)( 9,24)(10,12)(11,32)(13,18)(15,28)(17,26)(19,34)(20,23)(21,33)(25,30)(27,29)(31,35);
poly := sub<Sym(35)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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 >;