Wikipedia Talk:Penrose tiling

Multiple tilings and rotational symmetry

There are certainly finitely many connected tilings given any finite
number N of tiles, but there are uncountably many tilings of the
plane, using the deflation argument.  However, it is important to note
that only two of the tilings possess five-fold rotational symmetry.
This renders most of the statements about five-fold symmetry false.
It should be mentioned that these two, and uncountably many others,
also possess mirror symmetry; only the two rotationally-symmetric ones
possess mirror symmetry through more than one line.  The distinction
between finite and infinite tilings is crucial here, since a finite
subtiling cannot be used to determine which infinite tiling you are
in, nor even where you are in that infinite tiling.

Statements about a "rule" that no two rhombs can form a parallelogram
are also incorrect, as noted above.  The true rule can be seen in the
diagram; color the edges of the rhombs as in that diagram, and only
allow matching-colored edges to be adjacent.

There doesn't seem to be a rating for an article that has quite a bit
of good stuff and some glaring falsehoods.  -Dan Hoey 02:28, 24 April
2007 (UTC)