Complexity of union (computational geometry)
The complexity of a union of objects is the number of pieces in the boundary of the union. In the plane "complexity of boundary" is equivalent (upto a constant factor) to "number of vertices". But in general the boundary complexity is the sum of complexities of all objects needed to describe the boundary (vertices, edges, faces, and so on). It's just that in the plane the number of vertices in the boundary is the same as the number of edges (because the boundary is a set of cycles in this case)