Regular Tilings

Much of the material presented here has been taken from the book A Puzzling Journey to the Reptiles and Related Animals, privately published by the author in 1987.

Many trivial and some very difficult tilings have been omitted. For each shape only one interesting tiling has been selected.

Some of the tilings, especially the odd tilings, are difficult to find.

The challenge selection shows you various areas to fill and the tile to fill it with.

You draw a tile by a stamping method: Drag the sample tile with the locator to the desired position on the board. (The locator is initially positioned at the top-right corner.) Click the color selection to select the tile's color. Use the "rotations and reflections" slider to select the orientation of the tile. Now click the "store new tile" button. The new tile will be displayed from now on. You can now use the locator-tile to stamp the next tile.

Using the "show stored polygons" slider and the "delete last shown" button, you can delete any stored polygon at any time.

This Demonstration stores all setups you create. Hence you can come back to a half-solved challenge at any time.

Michael Reid: solution to problems 10, 11, 12, and 14.
David Klarner: solution to problem 4.