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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 ...
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]
Denis Weaire (1984), a theoretical physicist, proposed a counter-example to Lord Kelvin's conjecture on which surface was the most economical way to divide space into cells of equal size with the least surface area. This counter-example is now referred to as the Weaire–Phelan structure.
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 ...
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 ...
Using the Weaire–Phelan geometry, the Water Cube's exterior cladding is made of 4,000 ETFE bubbles, some as large as 9.14 meters (30 ft) across, with seven different sizes for the roof and 15 for the walls. [15] The structure had a capacity of 17,000 during the games. [11]
Cubic honeycomb. In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n -honeycomb for a honeycomb of n -dimensional space.