How does this mirror NOT flip its image? Years ago, Professor Andrew Hicks invented a mirror that doesn't flip its image.
I know it was done via computer modeling to make light traverse specific paths, but that sounds basically like black magic -- I don't understand how it works from an optics standpoint.
Can someone please explain how it actually works, hopefully with a diagram?
 A: As mentioned in the comments, Dr. Hicks published a brief explanation of the mathematical construction he uses in Physics Today ["The customized reflections of freeform mirrors," Phys. Today, Oct. 2010, p. 72].  Here's a link for those who have access.  Beware, however, that his idea of image formation by mirrors in incorrect - he indicates that the image in a plane mirror can lie in front of the mirror, in the same plane as the object, for instance.  But the gist is this:  Imagine observing the mirror image through a fixed pinhole, representing the pupil of a camera or the observer's eye.  A light ray that emanates from a point q on the object (the person's right hand, say) bounces off the mirror and then goes through the pinhole, but it must approach the pinhole from a point p in the same plane as the object, but on the left.  That tells you where to place a small segment of the mirror, and at what angle - it has to lie along the vector from the pinhole through p, and depending on its distance in the x direction (away from the pinhole), it has to be at an angle to deflect a ray from q through p and through the pinhole.  If you can construct a continuous surface that does that for every point q on the object, you've got your "reversing" mirror.  The solution is not unique, and he says it can only be done approximately.  He doesn't give the details of his solution, but says it's "saddle shaped," and works within 3 cm of the optical axis, for objects 34 ± 1 cm from the mirror.
Note that ordinary plane mirrors do NOT reverse the image.  The reason text appears reversed in the mirror is because you turn the text around to present it to the mirror.  (If the text were on a transparency, you would see the text the same way both on the object and on its image in the mirror.) So this device actually DOES flip its image, which is what makes it special.  Note also that a mirror that is a concave parabola horizontally should work similarly for objects farther than its focal length, though it won't in general preserve the size of the image, except if the image is at the right distance from the mirror.  (But then, I suspect Dr. Hicks' probably wouldn't either...)
A: Well it is a mirror, meaning a reflective surface, but the shape of it matters very much for the image. The funny reflections in a mirror house are in some cases the result of multiple shapes given to the reflecting surface.
The following image is taken from his patent online

Where the observer (represented by the eye O) and the reflected rays are shown (maybe is somewhat misleading the direction of the arrows on the drawing, I would put them going from the screen, towards the eye). 
So the idea is that the reflecting surface is concave-like in the cut shown, but probably flat in the cut perpendicular. So it flips the image only on the left-right direction (like a typical concave mirror) but not so in the up-down direction.
Of course, the computation is needed because the surface that behaves like so is not a simple one (circular nor ellipse nor any simple) and has to be calculated, also in a way such to avoid distortion of the image as possible.
