In 2 dimensions, the most efficient packing mechanism is an array of hexagons - a honeycomb. In 1887, William Thomson (Lord Kelvin) asked the question 'What is the most efficient 3-D packing system?“
See (the original paper) : On the Division of Space with Minimla Partitional Area
He suggested that it was the 'bitruncated cubic honeycomb' which, until 1993, was widely recognised as the most efficient possible.
It was succeeded, however, by the Weaire–Phelan Structure (see Wikipedia) - found by computerised simulations of foam generation - which is currently the most efficient form yet found.
The question of whether the Weaire–Phelan Structure is the most efficient 3-D packing structure - having the smallest surface area per cell - is however still open. Subsequent mathematical simulations suggest that it is optimal - but this remains unproven.
Also see :
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