Thanks Hunter,
For the extra work, opening a new thread.
I can see it at scene frame 31 and while the clip is at 14 seconds.
A typical misbehavior in rare cases of the Boole Object. Not nice.
Try this:
Switch in the Boole [Attribute Manager] from High Quality to none.
or
Increase the segments of the cube, in various ways.
.
If one or the other (perhaps both) will not work, would you mind to share a link with a scene file, just the three polygons and the Cube in question. I will have a look into it.
(As a side note, typically the render engine puts it into triangles and changes the results sometimes, so since my idea of C4D is the result, I would try to render a preview.)
Let me know how it works, and we go from there.
My best wishes