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QuasiTiler draws Penrose tilings and their generalizations. This document explains the interesting geometry involved in the processes. The concepts involved are surprisingly simple. The only apparent hurdle that we have to overcome is working in spaces with more than 3 dimensions. However in the next section we start with examples in 2 and 3 dimensions where our intuition is useful. Then we extend the same concepts to more dimensions. I hope that you get some insight on the geometry of higher-dimensional spaces by reading this document and by experimenting with QuasiTiler. Includes interactive applet.

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