Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,2,10,6}

Atlas Canonical Name {6,2,10,6}*1440

Overview

Group
SmallGroup(1440,5924)
Rank
5
Schläfli Type
{6,2,10,6}
Vertices, edges, …
6, 6, 10, 30, 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

2-fold

3-fold

5-fold

6-fold

9-fold

10-fold

12-fold

15-fold

18-fold

20-fold

30-fold

45-fold

Covers minimal covers in bold

None in this atlas.

Representations

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