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Weaire–Phelan structure. In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum ...
Denis Weaire. Denis Lawrence Weaire FRS (born 17 October 1942 in Dalhousie, Simla, India) [1] is an Irish physicist and an emeritus professor of Trinity College Dublin (TCD). [2] Educated at the Belfast Royal Academy and Clare College, Cambridge (BA 1964, PhD 1968) he held positions at University of California, University of Chicago, Harvard ...
A network model of a primitive cubic system. The primitive and cubic close-packed (also known as face-centered cubic) unit cells. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
The mathematical topics described in the book include sphere packing (including the Tammes problem, the Kepler conjecture, and higher-dimensional sphere packing), the Honeycomb conjecture and the Weaire–Phelan structure, Voronoi diagrams and Delaunay triangulations, Apollonian gaskets, random sequential adsorption, and the physical ...
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Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules. These rules can be varied. Common ones are that there must be no gaps between tiles, and that no corner of one tile can lie along the edge ...
Tetrastix arrangement showing 6 sticks in each direction. In geometry, it is possible to fill 3/4 of the volume of three-dimensional Euclidean space by three sets of infinitely-long square prisms aligned with the three coordinate axes, leaving cubical voids; [1] [2] John Horton Conway, Heidi Burgiel and Chaim Goodman-Strauss have named this structure tetrastix.
No better solution was found until 1993 when Denis Weaire and Robert Phelan proposed the Weaire–Phelan structure; the Beijing National Aquatics Center adapted the structure for their outer wall in the 2008 Summer Olympics. [12]