# Pigeon principle question: Nine points in a diamond

A diamond (a parallelogram with equal sides) is given, and its sides are 2 cm long. The sharp angels are 60 degrees. If there are nine points inside the diamond, prove that there must be two of them so that the distance between them is at most 1 cm.

Ideas where to start from?

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Nine points and the pigeonhole principle suggests trying to find 8 "pigeonholes" for nine points. – Mark Bennet Jun 9 '12 at 17:25
Your diamond is a two-dimensional figure, I think? – Mark Bennet Jun 9 '12 at 17:27
I believe that “a parallelogram with equal sides” is usually called a “rhombus”. – MJD Jan 16 '14 at 17:51

The diamond may be a regular tetrahedron of side $2$. – André Nicolas Jun 9 '12 at 19:00