Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,10}

Atlas Canonical Name {2,6,10}*240

Overview

Group
SmallGroup(240,202)
Rank
4
Schläfli Type
{2,6,10}
Vertices, edges, …
2, 6, 30, 10
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

3-fold

5-fold

6-fold

10-fold

15-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

Representations

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