Great picture, Fredrick! Yes, a binary relation on \\(S\\) is the same as a subset of \\(S \times S\\), so the poset of binary relations on \\(S \\) is just our friend the power set \\( P(S \times S\\). So, it looks like an \\(n^2\\)-dimensional cube if \\(S\\) has \\(n\\) elements. You're taking \\(n = 2\\) so your picture looks a lot like this: