how to rotate a polygon along any axis

Question

I need to rotate a simple 2D polygon along any axis (to mimic 3D rotation).  The polygon is draw on a canvas using lines (VS 2010). I need to keep track of all coordinates during rotation.

I was able to write code for rotating an hexagone around x or y axis using simple math where theta is the angle from the plane XY axis, Phi from the XZ plane.

(rotating around x axis)
pt.X = ptCentre.X + r * cos(theta);
pt.Y = ptCentre.Y + r * sin(theta) * cos(Phi);

(rotating around y axis)

pt.X = ptCentre.X +  r * sin(theta) * cos(Phi);
pt.Y = ptCentre.Y + r * cos(theta);

This will not work for rotating the hexagon at 45 degree angle. I am not able to find the math/code for doing rotations at any angle, not just around x or y axis.