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In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex. It has Schläfli symbol of ' or ''t'' (as a truncated triangular tiling). Conway calls it a hextille. The internal angle of the hexagon is 120 degrees so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. == Applications == The hexagonal tiling is the densest way to arrange circles in two dimensions. The Honeycomb conjecture states that the hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making beehives (or rather, soap bubbles) was investigated by Lord Kelvin, who believed that the Kelvin structure (or body-centered cubic lattice) is optimal. However, the less regular Weaire-Phelan structure is slightly better. Chicken wire consists of a hexagonal lattice of wires. This structure exists naturally in the form of graphite, where each sheet of graphene resembles chicken wire, with strong covalent carbon bonds. Tubular graphene sheets have been synthesised; these are known as carbon nanotubes. They have many potential applications, due to their high tensile strength and electrical properties. File:Kissing-2d.svg |The densest circle packing is arranged like the hexagons in this tiling File:Chicken Wire close-up.jpg |Chicken wire fencing File:Graphene xyz.jpg |Graphene File:Carbon nanotube zigzag povray.PNG |A carbon nanotube can be seen as a hexagon tiling on a cylindrical surface The hexagonal tiling appears in many crystals. In three dimensions, the face-centered cubic and hexagonal close packing are common crystal structures. They are the densest known sphere packings in three dimensions, and are believed to be optimal. Structurally, they comprise parallel layers of hexagonal tilings, similar to the structure of graphite. They differ in the way that the layers are staggered from each other, with the face-centered cubic being the more regular of the two. Pure copper, amongst other materials, forms a face-centered cubic lattice. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hexagonal tiling」の詳細全文を読む スポンサード リンク
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