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The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3]
Nonmetallic material, or in nontechnical terms a nonmetal, refers to materials which are not metals. Depending upon context it is used in slightly different ways. In everyday life it would be a generic term for those materials such as plastics, wood or ceramics which are not typical metals such as the iron alloys used in bridges.
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
Unless otherwise noted, this article describes the stable form of an element at standard temperature and pressure (STP). [b]While arsenic (here sealed in a container to prevent tarnishing) has a shiny appearance and is a reasonable conductor of heat and electricity, it is soft and brittle and its chemistry is predominately nonmetallic.
The chemical elements can be broadly divided into metals, metalloids, and nonmetals according to their shared physical and chemical properties.All elemental metals have a shiny appearance (at least when freshly polished); are good conductors of heat and electricity; form alloys with other metallic elements; and have at least one basic oxide.
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection.
The use of the word "tiling" is problematic as well, despite its straightforward definition. There is no single Penrose tiling, for example: the Penrose rhombs admit infinitely many tilings (which cannot be distinguished locally). A common solution is to try to use the terms carefully in technical writing, but recognize the widespread use of ...