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 'bi-truncated 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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