PolygonIntersections is an option for Graphics3D which specifies whether intersecting polygons should be left unchanged.
With the default setting PolygonIntersections -> True, Graphics3D objects are returned unchanged whether or not they contain intersecting polygons.
With the setting PolygonIntersections -> False, Graphics3D objects are modified by breaking polygons into smaller pieces which do not intersect each other.
PolygonIntersections -> False is useful in creating graphics objects which can be sent to certain external three-dimensional rendering programs.
See The Mathematica Book: Section 2.9.14.
See also: RenderAll.