It is a corner: a point where three of more faces meet.
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For every polyhedron, there is a dual which is a polyhedron that has:a face where the first had a vertex,a vertex where the first had a face,the same number of edges.A self-dual polyhedron is a polyhedron whose dual is the same shape.All pyramids, for example, are self-dual.
It may be called an apex, but that is really only appropriate for a simple convex polyhedron.
Vertex
pyramid
The vertex is a point of polygon or polyhedra that is formed by 2 lines or 3 edges on a polyhedron.