The minimum set of axes you need to test are all those at right angles to the faces of the polyhedra. If none of these have an overlap the shapes are disjoint.

To get a left hand right angle vector for x, y, you simply use -y, x.

[EDIT - bit more info now not on phone ]

Assuming 2D here, you can loop through each shape and construct a vector from each vertex to the next one (B - A, C - B etc where the vertices are in A, B, C... order). If you then do the -y, x trick you end up with vectors pointing outwards at right angles from each face. These vectors represent the axes you need to test by projecting the vertices of each shape onto them and then comparing the min-max of each projection to see if they overlap.

You can ignore any axes that are equivalent to those that are already being tested, including any that point in the exact opposite direction as well as those which point in the same direction. It is common to precalculate these axes so you can trim out these duplicates as a post-processing step.

**Edited by Aardvajk, 08 June 2014 - 03:25 PM.**