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Number of Horizontal Rhombuses

How many horizontal rhombuses are there? Is there a rule for this?

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A calisson is a French sweet in the shape of two equilateral triangles edge to edge. They are packed in a hexagonal box. The puzzle is to show why the number of callisons pointing in each direction, in a fully packed box, must always be equal.
Reference
[1] D. Wells, The Penguin Book of Curious and Interesting Puzzles, New York: Penguin Books, 1993 p. 133.

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 Izidor Hafner
"Number of Horizontal Rhombuses"
 http://demonstrations.wolfram.com/NumberOfHorizontalRhombuses/
 Wolfram Demonstrations Project
 Published: December 20, 2012
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