Does every set of any three vertices of a cube determine a right triangle?

Question

I recently came across this in my textbook:

Any three vertices of a cube determine a right triangle. Is this a true statment?

My initial thought was that is was, but the answers say otherwise. I cannot, however, come up with a counterexample.

What three vertices of a cube don't determine a right triangle?

Answer 1

You are standing at a corner. Consider the three corners closest to you.

These three corners determine a triangle, all of whose sides are face diagonals. So all these sides have equal length, the triangle is equilateral.

Answer 2

Hint: Draw the cube so that it looks like a hexagon.

Answer 3

Three that involve no edges from the cube. If the vertices are the standard ones for the unit cube, then, $(0,0,0)$, $(0,1,1)$, and $(1,1,0)$ will do.