Kites and Darts are a type of non-periodic tiling invented by Roger Penrose. The tiles cover the plane in an infinite variety of beautiful, non-repeating patterns. The Golden Ratio (1/2)*(1+sqrt(5)) features prominently in the tiles, in their construction and in their patterns. In the limit, the ratio of kites to darts is the golden ratio. So if you print 1000 darts you should print 1618 kites. There are seven ways the tiles can be arranged around a vertex. These seven patterns were given names by John Conway and appear in the stl files: sun, star, ace, deuce, jack, queen, king.

The circular markings show how the edges of the tiles line up. The circular patterns themselves are interesting, and if you want you can print and use only the markings.

See these links for more information:
intendo.net/penrose/info.html
mathworld.wolfram.com/PenroseTiles.html
en.wikipedia.org/wiki/Penrose_tiling

This is a parametric openscad script that will generate a tile. The tile has notches in it that will mesh with other copies of the tile. This will allow you to print out and assemble a rectilinear box of any size/shape. (with the adhesive of your choice)

Particularly useful if you want to make a box that's too big to fit inside the build volume of your printer.

while you can just print out the components of a box, you can also use some of the optional sections of the code to add functional features to the tiles.

1) A button. Basically, this feature allows you to weaken a particular area so that when you press on it the plastic deforms and presses a button inside.

2) Cips. You can add little clips to the tips of some of the notches so that instead of being a solid box it can have a lid that easily attaches and detaches.

3) A platform. The clips need a bit of clearance to work properly, so the bottom of the box (that's mounted to something) should be raised up off of the mounting surface.

4) Fan mount. If the tile is big enough, you can add a hole (plus four screw holes) and mount a 40mm fan.

I modified the tileset uploaded by jmne to allow for different kinds of acrylic for each tile type. The result is a nice colourful set of lasercut puzzle-connected tiles for Settlers of Catan.

An update to the scad file to include
- a parametric symmetric joint, consisting of a combined male+female connector.
- a parametric symmetric span, having a combined male+female connector on each end.
- a parametric symmetric tile, having a combined male+female connector on each side.
- a parametric rectangle with symmetric connectors, having a combined male+female connector on each side.

Feel free to flattr this design or any derivatives if it was useful for you.

update: 2011-02-08 16:04 - some of the parameters were not used correctly, resulting in asymmetry if you changed the settings. Should be fixed now.

This item replaces the hexagonal tiles in Settlers of Catan with tiles that interlock. It will produce the 19 hexagonal tiles that comprise the basic set, as well as a bunch of tokens to represent the ports.

Can this shape tile the plane? It is not easy to guess by just putting the shapes together. With a little thought however there is an easy proof. It can't. How far can it go though? How many rings of tiles can you build around a first one. This is called the Heesch number of the tiling.

This shape is a world record holder you need 20 tiles before it will tile the plane periodically (10 up to symmetry). It fits together in an amazing variety of ways but can easily block itself. Making it a fun puzzle.

The tiles were found by a massive computer search by Joseph Myers. Look for this and other puzzling shapes at: srcf.ucam.org/~jsm28/tiling/

The idea to make physical tiles was originally from Chaim Goodman-Strauss: mathbun.com