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In Euclidean geometry, a plane is a flat two- dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space . A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin. While a pair of real numbers suffices to describe points on a plane, the ...
Uniform colorings. There are a total of 32 uniform colorings of the 11 uniform tilings: Triangular tiling – 9 uniform colorings, 4 wythoffian, 5 nonwythoffian. Square tiling – 9 colorings: 7 wythoffian, 2 nonwythoffian. Hexagonal tiling – 3 colorings, all wythoffian. Trihexagonal tiling – 2 colorings, both wythoffian.
A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Several notions of a plane may be defined.
Material properties of diamond. Burns above 700 °C in air. Diamond is the allotrope of carbon in which the carbon atoms are arranged in the specific type of cubic lattice called diamond cubic. It is a crystal that is transparent to opaque and which is generally isotropic (no or very weak birefringence ).
The rhombus has a square as a special case, and is a special case of a kite and parallelogram. In plane Euclidean geometry, a rhombus ( pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.
In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α-tin, the semiconductors silicon and germanium, and silicon–germanium alloys in any proportion.
The Euclidean case. The triangle group is the infinite symmetry group of a certain tessellation (or tiling) of the Euclidean plane by triangles whose angles add up to π (or 180°). Up to permutations, the triple ( l , m , n) is one of the triples (2,3,6), (2,4,4), (3,3,3). The corresponding triangle groups are instances of wallpaper groups .
Euclidean plane isometry. In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below § Classification ).