In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes...

dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together,...

surface area. This counter-example is now referred to as the Weaire–Phelan structure. This structure was an integral part of the design of the aquatic centre...

1993 when Denis Weaire and Robert Phelan proposed the Weaire–Phelan structure; the Beijing National Aquatics Center adapted the structure for their outer...

hexagonal trapezohedron and truncating the polar axis vertices. The Weaire–Phelan structure contains another form of this polyhedron that has D2d symmetry...

higher-dimensional sphere packing), the Honeycomb conjecture and the Weaire–Phelan structure, Voronoi diagrams and Delaunay triangulations, Apollonian gaskets...

uniform honeycombs, another well known example is the Weaire–Phelan structure, adopted from the structure of clathrate hydrate crystals Documented examples...

Choe who proved that the optimal figure is an irregular hexagon. Weaire–Phelan structure, a counter-example to the Kelvin conjecture on the solution of...

the Kelvin structure, and this was widely believed for over 100 years, until disproved in 1993 by the discovery of the Weaire–Phelan structure. The surprising...

Includes an optimal space-filling shape in foams (see Weaire–Phelan structure) and in the crystal structure of clathrate hydrate (see illustration, next to...

century, a mathematical description of the structure is still debated. The computer-generated Weaire–Phelan structure is the most recent. In a reticulated foam...

based on the Weaire–Phelan structure, a structure devised from the natural pattern of bubbles in soap lather. In the true Weaire–Phelan structure the edge...

(β-phase) Weaire–Phelan structure, for the space tessellation generated by A15 phases Frank, F. C.; Kasper, J. S. (1959-07-10). "Complex alloy structures regarded...

partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem Lebesgue's universal covering...

very slightly curved faces. In 1993, Denis Weaire and Robert Phelan proposed the Weaire–Phelan structure, which uses less surface area to separate cells...

length) for perfect natural pyrite (also the pyritohedron in the Weaire–Phelan structure). Another one is h = ⁠1/φ⁠ = 0.618... for the regular dodecahedron...

three-dimensional tessellations, also called honeycombs.[citation needed] The Weaire–Phelan structure is reported in one primary philosophical source to be the best...

truncated trapezohedron (51262). Together, they form a version of the Weaire–Phelan structure. Typical guests forming Type I hydrates are CO2 in carbon dioxide...

Surface Evolver Stretched grid method Tensile structure Triply periodic minimal surface Weaire–Phelan structure Meeks, William H. III; Pérez, Joaquín (2011)...

dodecahedral honeycomb Disphenoid tetrahedral honeycomb Others: Weaire–Phelan structure periodic space-filling honeycomb with irregular cells Abstract...

body-centered cubic lattice) is optimal. However, the less regular Weaire–Phelan structure is slightly better. The hexagonal tiling is commonly found in nature...

least surface area. This counter-example is now referred to as the Weaire–Phelan structure. Mike Coey (2007) is a renowned experimentalist in the area of...

the A15 phases, which forms the polyhedral approximation of the Weaire–Phelan structure. The Wigner–Seitz cell always has the same point symmetry as the...

Plateau Stretched grid method Tom Noddy The Amazing Bubble Man Weaire–Phelan structure Hutchings, Michael; Morgan, Frank; Ritoré, Manuel; Ros, Antonio...

In materials science, a metal foam is a material or structure consisting of a solid metal (frequently aluminium) with gas-filled pores comprising a large...

Example cubic structures (221) Caesium chloride. Different colors for the two atom types. (216) Sphalerite (223) Weaire–Phelan structure The symbol e {\displaystyle...

Strukturbericht type is a system of detailed crystal structure classification by analogy to another known structure. The designations were intended to be comprehensive...

dodecahedral honeycomb Others Trapezo-rhombic dodecahedral honeycomb Weaire–Phelan structure Convex uniform honeycombs in hyperbolic space Order-4 dodecahedral...

three-dimensional space groups and examples of honeycombs such as the Weaire–Phelan structure. It also considers the symmetries of less familiar geometries:...

found to be more efficient foams of soap bubbles, among which the Weaire–Phelan structure appears to be the best. The honeycomb represents the permutohedron...