Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,6}

Atlas Canonical Name {3,6}*36

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Overview

Group
SmallGroup(36,10)
Rank
3
Schläfli Type
{3,6}
Vertices, edges, …
3, 9, 6
Order of s0s1s2
6
Order of s0s1s2s1
6
Also known as
{3,6}(1,1). if this polytope has another name.

Special Properties

  • Toroidal
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

Covers minimal covers in bold

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Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5)(6,9)(7,8);;
s1 := (1,6)(2,4)(3,8)(5,7);;
s2 := (4,5)(6,7)(8,9);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(9)!(2,3)(4,5)(6,9)(7,8);
s1 := Sym(9)!(1,6)(2,4)(3,8)(5,7);
s2 := Sym(9)!(4,5)(6,7)(8,9);
poly := sub<Sym(9)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References

None.

to this polytope.

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