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mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Z n {\displaystyle \mathbb {Z} ^{n}} , is the lattice in the Euclidean space R n...5 KB (516 words) - 09:52, 5 April 2024
Trihexagonal tiling (redirect from Kagome lattice)tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. It consists of equilateral triangles and regular hexagons, arranged so...16 KB (1,625 words) - 20:35, 27 October 2024
sided polygon (heptagon) and the number 7 at the centre indicate the seven lattice systems. The inner heptagons indicate the lattice angles, lattice parameters...21 KB (2,438 words) - 01:16, 19 August 2024
Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...31 KB (1,998 words) - 17:29, 22 September 2024
Pick's theorem (category Theorems about polygons)lattice points in symmetric convex sets. This already proves Pick's formula for a polygon that is one of these special triangles. Any other polygon can...20 KB (2,337 words) - 22:22, 17 August 2024- arbitrary lattice polygon (one drawn on a grid with vertically and horizontally adjacent lattice points at equal distances, and with vertices on lattice points)...20 KB (3,530 words) - 09:55, 20 September 2024
Voronoi diagram (redirect from Voronoi polygon)Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical...46 KB (5,497 words) - 02:50, 3 November 2024
Convex polytope (redirect from Face lattice)half-planes), a shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon. Special cases of an unbounded convex polytope...23 KB (3,266 words) - 17:46, 21 May 2024- _{D}}e^{-2Lr-2Ks}} summing over all polygons in the dual lattice, where r and s are the number of horizontal and vertical lines in the polygon, with the factor of 2...11 KB (1,792 words) - 22:44, 7 July 2024
These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons. The sum of external angles of a simple polygon is...31 KB (3,199 words) - 01:11, 17 October 2024- n} -sided polygons with up to ten sides are able to tile a plane-vertex alongside other regular polygons alone; the first regular polygon unable to do...22 KB (2,487 words) - 06:40, 29 October 2024
- surface is conformally equivalent to a torus C/Λ for some lattice Λ in C. The fundamental polygon of Λ, if assumed convex, may be taken to be either a period...43 KB (5,997 words) - 21:52, 15 October 2024
crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined...16 KB (2,354 words) - 15:40, 17 October 2024
Partition of a set (redirect from Partition lattice)polygon (whose vertices are the elements of the block). The partition is then noncrossing if and only if these polygons do not intersect. The lattice...14 KB (1,881 words) - 12:46, 26 August 2024
Pentagon (category Constructible polygons)Greek πέντε (pente) 'five' and γωνία (gonia) 'angle') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°....23 KB (3,048 words) - 15:40, 8 October 2024
Today he is best known for Pick's theorem for determining the area of lattice polygons. He published it in an article in 1899; it was popularized when Hugo...4 KB (339 words) - 00:01, 16 September 2024- ISBN 0-88385-511-9. Poonen, Bjorn; Rodriguez-Villegas, Fernando (March 2000). "Lattice Polygons and the Number 12" (PDF). American Mathematical Monthly. 107 (3): 238–250...39 KB (4,352 words) - 23:19, 3 November 2024
- by any point of a lattice and the slope of the lines, Pick's theorem relating the area of a lattice polygon to the number of lattice points it contains...6 KB (664 words) - 02:16, 14 February 2021
A regular dodecahedron (grey) approximated with a lattice polygon using the rule of twelfths (red)...10 KB (1,002 words) - 04:01, 15 September 2024
Parallelogram (section Lattice of parallelograms)where a and b are the lengths of adjacent sides. Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice...15 KB (1,996 words) - 03:44, 28 October 2024
- simple lattice-sphere with irregular polygonal meshes, which are for the most part pentagonal and about four times as broad as the polygonal meshes of
- number of objects using three types of lattice structure: suspension, vaulted and rigid spatial shell. Suspension lattice structures... were based on tension
- 24-bit color image grid tiling tesselation of the plane Set partitions Lattice Mesh checkerboard see also: ruler axis 2D 3D classify grids is by their
