Maximum distance between two points on shape - name?

Question

What is the name for the maximum distance between two points lying on a geometric shape? For the circle, such a thing is obviously called "the diameter". Is it called "the diameter" for every other arbitrary shape as well?

Answer 1

Yes, for any set in a metric space, the supremum of the distances between its points is also called the diameter. See, e.g. Wikipedia's article.

Answer 2

The diameter keeps it name through geometric shapes, whereas the radius becomes known as the apothem.

Answer 3

This is an established meaning of the term in graph theory. Note that for an open region, "supremum" would technically be better than "maximum".