If $L$ is a finite lattice, then $L$ is determined by its subposet of elements that are join-irreducible or meet-irreducible (or both). In particular, if the only only join-irreducibles are atoms (vertices) and only meet-irreducibles are coatoms (facets), then $L$ is determined by the incidences between its vertices and facets. See for instance Exercise 3.27 of Enumerative Combinatorics, vol. 1, second edition.

If $L$ is a finite lattice, then $L$ is determined by its subposet of elements that are join-irreducible or meet-irreducible (or both). In particular, if the only join-irreducibles are atoms (vertices) and only meet-irreducibles are coatoms (facets), then $L$ is determined by the incidences between its vertices and facets. See for instance Exercise 3.27 of Enumerative Combinatorics, vol. 1, second edition.