====== The Kelvin problem (3-D packing) ======

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)  : [[http://soft-matter.seas.harvard.edu/images/1/17/Kelvin_Cell.pdf|On the Division of Space with Minimla Partitional Area]] {{:oa_padlock_grn.png?16&nolink|Open Access}}

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 [[https://en.wikipedia.org/wiki/Weaire%E2%80%93Phelan_structure|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.

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Also see : [[content:mathematics:ulam_packing]]