Here's a wireframe diagram of a scene with two flat rectangles, one red and one blue. In Modeler, they were SLICED through each other so that the part where they overlap became two polygons which occupy the same space. There is a big floor polygon to catch shadows, and a big spherical mirror in the background.

Here we see two ways Lightwave hates coplanar polygons. The reflection of the polygons is screwed up in the mirror and there are some red streaks on the blue polygon in the foreground. Both of these happen because Lightwave can't decide which polygon the light ray hits first.

This is fun: if we flip the blue polygons over, we can't see them because Double Sided is turned off. But, the reflection is still screwed up. We also see a different phenomenon: Lightwave rendered the wrong shadow! The shadow you see is under the blue polygon, and the red's shadow dissappeared! This isn't actually a bug. It's a property of single-sided polygons. LightWave traces shadow rays from the surface towards the light, so from the surface's point of view the opposite squares are visible.