This set of three tiles can cover the plane without any gaps or overlappings in an a-periodical way. The relative ratios of the three tiles appearing in a large covering of the plane are related to the Golden Ratio:
One : a half plus the square root of five : a half plus three tenths of the square root of five
You can order a box containing 36 heart-, 58 cloud- and 42 sun-tiles. If you are interested, send me an e-mail and I give you details about costs and sizes.
This puzzle-set is based on a mosaic that can be found in the Northern Dome of the Friday Mosque in Isfahan (first picture in the gallery below). The puzzle has two layers; the bottom layer is made out of wooden girih tiles showing the basic pattern. The top layer is the actual mosaic and has two contrasting colours.
The basic pattern consists of two types of hexagons. The mosaic itself has only four different types of tiles. One of these is a regular heptagon which is quite unique; there aren't many mosaics with regular heptagons.
There is another unique thing about this mosaic: In the National Library of Paris a manuscript can be found written somewhere in Persia in the sixteenth century. In this manuscript there is a drawing of a cell of the mosaic including some instructions on how to construct the cell. So far there are no other examples of Islamic mosaics that can be related to a manuscript this old in which the way to construct the mosaic is explained in a drawing and in writing.
The puzzle below is an a-periodic pattern made of the 'kite'and 'dart' shapes designed by Roger Penrose in the 1970's. The little incisions along the edges of the tiles relate to the 'matching rules' for creating an aperiodic pattern with a quasicristalline character.