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The official answer is, believe it or not, only two! Penrose used
a kite and a dart to tile the plane. They looked like this:
[add pictures of kite and dart]
There are lots of sites which deal with Penrose tilings on the web.
Here are some with good exercises:
- University of Idaho
- This is a good place to start. See if you can work out how
to tile the plane using the shapes they give.
- The Dr Matrix Programming Challenge
- The challenge is to create a Windows program which explores the properties of
Penrose Tiles. The site also has good background material.
And here are some others:
- The Geometry Junkyard
- Has lots of links and info
- The CRC Concise Encyclopedia of Mathematics
- Has good info and pictures of kites and darts.
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