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SimplicialComplexes :: facets

facets -- the facets of a simplicial complex



In Macaulay2, every simplicial complex is equipped with a polynomial ring, and the resulting matrix of facets is defined over this ring.

The 3-dimensional sphere has a unique minimal nonface which corresponds to the interior.

i1 : R = ZZ[a..e];
i2 : sphere = simplicialComplex monomialIdeal(a*b*c*d*e)

o2 = | bcde acde abde abce abcd |

o2 : SimplicialComplex
i3 : facets sphere

o3 = | bcde acde abde abce abcd |

             1       5
o3 : Matrix R  <--- R
The following faces generate a simplicial complex consisting of a triangle (on vertices a,b,c), two edges connecting c to d and b to d, and an isolated vertex e.
i4 : D = simplicialComplex {e, c*d, b*d, a*b*c, a*b, c}

o4 = | e cd bd abc |

o4 : SimplicialComplex
i5 : facets D

o5 = | e cd bd abc |

             1       4
o5 : Matrix R  <--- R
There are four facets of D.

Note that no computatation is performed by this routine; all the computation was done while constructing the simplicial complex.

A simplicial complex is displayed by listing its facets, and so this function is frequently unnecessary.

See also

Ways to use facets :

For the programmer

The object facets is a method function with options.