Editing Abstract polytope (section)

====Connectedness====
A poset P is '''connected''' if P has rank ≤ 1, or, given any two proper faces F and G, there is a sequence of proper faces

:H<sub>1</sub>, H<sub>2</sub>, ... ,H<sub>k</sub>

such that F = H<sub>1</sub>, G = H<sub>k</sub>, and each H<sub>i</sub>, i < k, is incident with its successor.

The above condition ensures that a pair of disjoint triangles '''abc''' and '''xyz''' is ''not'' a (single) polytope.

A poset P is '''strongly connected''' if every section of P (including P itself) is connected.

With this additional requirement, two pyramids that share just a vertex are also excluded. However, two square pyramids, for example, ''can'', be "glued" at their square faces - giving an octahedron. The "common face" is ''not'' then a face of the octahedron.