Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,4}

Atlas Canonical Name {4,4}*64

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Overview

Group
SmallGroup(64,138)
Rank
3
Schläfli Type
{4,4}
Vertices, edges, …
8, 16, 8
Order of s0s1s2
4
Order of s0s1s2s1
4
Also known as
{4,4}(2,2), {4,4}4. if this polytope has another name.

Special Properties

  • Toroidal
  • Locally Spherical
  • Orientable
  • Self-Dual
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

Covers minimal covers in bold

2-fold

3-fold

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25-fold

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31-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2> of order 2

6 facets

4 vertex figures

P/N, where N=<(s1*s2)^2> of order 2

4 facets

6 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 6)( 7,10)( 9,12)(11,14)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);;
s2 := ( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(16)!( 2, 3)( 4, 6)( 7,10)( 9,12)(11,14)(13,15);
s1 := Sym(16)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);
s2 := Sym(16)!( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);
poly := sub<Sym(16)|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, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle