Seems to fit that definition.
However facets, being parts of polytopes such as polygons and polyhedra, shouldn't generally line up in the dimension below that of there dimension. For example edges shouldn't be collinear, faces shouldn't be coplanar, and points shouldn't be in the same place as each other. Note that star polygons are still fine.
It might be desirable to be able to switch between an "abstract polytope" like approach where polytopes are made of a set of such parts, for example a square has 4 edges, 4 vertices, and a face. And an approach where the polygon is made of the points that form its edge, a little like how a circle is defined. This causes ambiguity if adjacent edges are aloud to be in a line, or if points can be the same place as each other.
On a somewhat related note, tilings generally avoid 2 edge vertices.