[amelius]

It's very easy to get 4 points on a circle. In 2d space just the four corners of a unit square would do it.

[Rhapso]

On a sphere or modulus space, that just becomes a K4, so it isn't even an edge case, it is the solution that the approximation would generate.

[amelius]

Yes, you definitely have to deal with it, in virtually any setup.