How do I distribute 5 points evenly onto an irregular shape?

Question

Here is a problem I am trying to solve:

I have an irregular shape. How would I go about evenly distributing 5 points on this shape so that the distance between each point is equal to each other?

Answer 1

David says this is impossible, but in fact there is an answer out of left field: just put all your points on top of each other! They'll all have the same distance to all the other points: zero.

In fact, that's the only algorithm that has a solution (i.e. all pairwise distances are the same) regardless of the input shape.

I know the question asks to put the points "evenly", but since that's not formally defined, I expect that was just an attempt to explain "all pairwise distances are the same", in which case my answer is "even".