I cannot really figure out what causes one surface to overlap another. In a 3D engine I'm creating, my technique is failing in edge cases.

My method is sorting the surfaces to be painted from the furthest to the closest. To determine the closeness, I'm comparing the average z values. Sometimes, however, an overlapping surface has a higher average z value than the one it is overlapping. Thus, the surface further away is painted over the closer one - resulting in bizarre rendering like this:

What one is meant to see is the purple front surface of the cube only, whilst the red side surface is painted over the purple one. The average z value of the purple surface is higher, and therefore 'further away'. So I'm having some doubt as to whether this technique is correct.

What I also tried is getting the distance from the camera (i.e. origin) to the surface, but then I needed a point. I chose the middle of each surface but also this doesn't always seem to work because not all surfaces are as large as each other.

Therefore, what is a reliable way to determine the order of closeness of surfaces towards the origin?