Medieval Islamic Tiling

Q: How do can you tile a surface with shapes that have 5-fold or 10-fold symmetry? (A square has 2-fold symmetry -- it's obviously easy to tile a surface with squares.) How can you do it without a compass or a straightedge (which, as the pattern becomes larger and more complex, would cause errors to accumulate and distort the pattern)? "Girih patterns" from 15th century Islamic architecture demonstrate how it's done.

PDF of a physics paper from Harvard figuring it out.