Imagine a plane that intersects three edges of a rectangular prism. There are three possibilities:
the plane intersects the prism at points equidistant from a common vertex, forming an equilateral triangle.
the plane intersects the prism at 2 points equidistant from a common vertex, and intersects a third edge at a different distance from the same vertex, forming an isosceles triangle.
the plane intersects the prism at points that are all at different distances from a common vertex, forming a scalene triangle.
