Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6}

Atlas Canonical Name {4,6}*72

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Overview

Group
SmallGroup(72,40)
Rank
3
Schläfli Type
{4,6}
Vertices, edges, …
6, 18, 9
Order of s0s1s2
4
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Self-Petrie

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

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Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := (5,6);;
s1 := (1,2)(3,5)(4,6);;
s2 := (2,3)(5,6);;
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*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(6)!(5,6);
s1 := Sym(6)!(1,2)(3,5)(4,6);
s2 := Sym(6)!(2,3)(5,6);
poly := sub<Sym(6)|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*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0 >;

References

None.

to this polytope.

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