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Very very nice! After looking at the "house" shape (polygon #10 in the first EDIT section) more closely I realized it was being drawn correctly. I can now see that I will have to add an area check to weed out results that have area not equal to n times a unit triangle. Again, thanks so much Silvia.
π/180 got rid of the Floor[] errors. ty. If you use the order-3 sets as input, you will see that the squares with the 'X' in the center have hypotenuses of length 1, rather than length $\sqrt 2$. And there is a similar problem with the "house" shape. Is that error coming from the If[] statement, do you think?