Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,4}

Atlas Canonical Name {6,4}*48a

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Overview

Group
SmallGroup(48,38)
Rank
3
Schläfli Type
{6,4}
Vertices, edges, …
6, 12, 4
Order of s0s1s2
12
Order of s0s1s2s1
2
Also known as
{6,4|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

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Covers minimal covers in bold

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Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 3, 4)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(12)!( 3, 4)( 6, 7)( 9,10)(11,12);
s1 := Sym(12)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);
s2 := Sym(12)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);
poly := sub<Sym(12)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle