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'Shaping Up' printed from http://nrich.maths.org/

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For this activity, you'll need to print out these cards. There are 27 different cards in total. Here is a picture of just three of them:

three sample cards

What rules were used to make the 27 cards, do you think?
Have all the possible combinations of two shapes been included?
How do you know?

If the rules were changed so that a card has two triangles, what would the complete set of cards contain?

This problem is based on ideas from "It Makes You Think", a book and CD of mathematical puzzles and problems, produced by Jill Mansergh and available from The Association of Teachers of Mathematics (ATM)