Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,2,30,2}

Atlas Canonical Name {8,2,30,2}*1920

Overview

Group
SmallGroup(1920,235336)
Rank
5
Schläfli Type
{8,2,30,2}
Vertices, edges, …
8, 8, 30, 30, 2
Order of s0s1s2s3s4
120
Order of s0s1s2s3s4s3s2s1
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

4-fold

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

20-fold

24-fold

30-fold

40-fold

60-fold

Covers minimal covers in bold

None in this atlas.

Representations

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