From: steve edwards <sedwards@spsu.edu>
Subject: Re: penrose tiles
Date: Sun, 02 Jan 2000 12:38:34 -0500
Newsgroups: sci.math

The Penrose kite and dart tile periodically if you put them together to make a
parallelogram, actually a rhombus.  In order to have them tile nonperiodically,
you must insist that they be put together NOT in that fashion.

You can alter the kite and dart to get the penrose rhombs, which also
tile aperiodically.  I don't know of any pairs of tiles, unrelated to
Penrose's which tile aperiodically.  Robinson and Penrose both came up
with sets of six which are aperiodic.  It is an open question whether
any one tile can tile aperiodically.

You can find all the info in "Tiling and Patterns", by Grunbaum and Shephard,
out of print but available at used places.
I have a small site on this subject at
      http://www2.spsu.edu/math/tiling/index.html
and some links at  http://www2.spsu.edu/math/edwards/courses/links.html

Steve Edwards

[text reformated --djr]