Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,10,2}

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

Overview

Group
SmallGroup(240,202)
Rank
4
Schläfli Type
{6,10,2}
Vertices, edges, …
6, 30, 10, 2
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 := ( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);;
s1 := ( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30);;
s2 := ( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);;
s3 := (31,32);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(32)!( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);
s1 := Sym(32)!( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30);
s2 := Sym(32)!( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);
s3 := Sym(32)!(31,32);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;