- Usage:
`facets D`

- Inputs:
`D`, a simplicial complex

- Optional inputs:
- useFaceClass => ..., -- Option to return faces in the class Face

- Outputs:
- a matrix, with one row, whose entries are squarefree
monomials representing the facets (maximal faces) of
`D`

- a matrix, with one row, whose entries are squarefree
monomials representing the facets (maximal faces) of

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

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`.

There are four facets of `D`.

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 |

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 |

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.

- SimplicialComplexes -- simplicial complexes
- simplicialComplex -- create a simplicial complex
- faces -- the i-faces of a simplicial complex

- facets(SimplicialComplex)