In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the Weaire–Phelan structure is a complex 3-dimensional structure representing an idealised foam

Foam

-Definition:A foam is a substance that is formed by trapping gas in a liquid or solid in a divided form, i.e. by forming gas regions inside liquid regions, leading to different kinds of dispersed media...

 of equal-sized bubbles. In 1993, Trinity College Dublin physicist Denis Weaire

Denis Weaire

Denis Lawrence Weaire is an Irish physicist, who is an emeritus professor of Trinity College Dublin.Educated at the Belfast Royal Academy and Clare College, Cambridge, he has since held positions at the universities of California, Chicago, Harvard and Yale, ultimately holding professorships at...

 and his student Robert Phelan found that in computer simulations of foam, this structure was a better solution of the "Kelvin problem" than the previous best-known solution, the Kelvin structure.
In 1887, Lord Kelvin asked how space could be partitioned into cells of equal volume with the least area of surface between them, i.e., what was the most efficient bubble foam?
This problem has since been referred to as the Kelvin problem.

He proposed a foam, based on the bitruncated cubic honeycomb

Bitruncated cubic honeycomb

The bitruncated cubic honeycomb is a space-filling tessellation in Euclidean 3-space made up of truncated octahedra.It is one of 28 uniform honeycombs. It has 4 truncated octahedra around each vertex....

, which is called the Kelvin structure. This is the convex uniform honeycomb

Convex uniform honeycomb

In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.Twenty-eight such honeycombs exist:* the familiar cubic honeycomb and 7 truncations thereof;...

 formed by the truncated octahedron

Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces , 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....

, which is a 14-sided space-filling polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 (a tetradecahedron

Tetradecahedron

A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces....

), with 6 square faces and 8 hexagonal faces.