tools - Illustrator rotational transformation is imperfect

So I created a simple hexagon using the polygon tool. When applying a 30° (360 / 6 / 2) rotation (to change its orientation) the anchor points are off by something what looks like a floating point rounding error.

So my question is, how do I rotate objects perfectly, so that the anchor points align with the grid again?

Steps to reproduce:

1. Create a hexagon (Polygon tool, 6 sides, 100 px radius)


2. Rotate it by 30° (Shift+F8)



3. Enable the grid and zoom in. The top and bottom anchor point will be noticeably off.

A rotation of 29.9° is actually closer to the desired result than 30°.