Friday, February 22, 2013

[riyrojee] Tessellating circles and spheres

Draw a circle in a square.  If the circle extends outside the square, it reenters from the other side as in a toroidal universe.  In other words, a tessellation with a square unit cell.

Pack N such identical non-overlapping circles in a square.  What is the largest radius for a given N?

Spheres in a cube.

Draw the Voronoi cell of each circle or sphere, yielding a polyhedral tessellation.

This has almost certainly been done, but I don't know the name of the problem.

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