to test whether a polygon tiles the plane periodically??

[Michael O'H <hanrahan398@yahoo.co.uk>]

Newbie-oid question here...

Might someone be kind enough to help me with code for testing whether a
polygon is capable of tiling the plane periodically?

The polygon needs to be input as a string of side-lengths and a string of
angles.

E.g. {{1,2,1,2},{Pi/2, Pi/2, Pi/2, Pi/2}} would yield "yes" because it's a
2x1 rectangle, which does tile the plane periodically. Ditto with any
quadrilateral.

{{1,1,1,1,1},{Pi/2, Pi/2, Pi/6, 5*Pi/3, Pi/6}} would yield "no" because it's
a square with an equilateral triangle bitten out of it, which does not tile
the plane periodically.

It has been proved that no algorithm will always find whether a polygon is
capable of tiling the plane (whether periodically or non-periodically); I am
only trying to study tilings which are definitely periodic. An algorithm
exists but I have been unable to find it or code to implement it.

Many thanks for any assistance with this! 

Michael O'H
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