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- Is the "hat" shape really a single shape?
Recently there's been a lot of publicity about the discovery of a single shape that tiles the plane in a non-repeating manner. These are similar to Penrose tilings, but just use a single shape, while the Penrose tilings used two shapes. However, as I've played with these, I've realized that some of the "hats" are mirror images of others. So is it really fair to consider it a single shape? See the attached illustration showing that some shapes are right-handed(RH) and some are left-handed(LH). Is there a true single shape (without mirror imaging) that can do this? I'd appreciate comments.