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Tetrakis Square Tiling
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is a square tiling with each square divided into four isosceles right triangles from the center point, forming an infinite arrangement of lines. It can also be formed by subdividing each square of a grid into two triangles by a diagonal, with the diagonals alternating in direction, or by overlaying two square grids, one rotated by 45 degrees from the other and scaled by a factor of √2. Conway, Burgiel, and Goodman-Strauss call it a kisquadrille, represented by a kis operation that adds a center point and triangles to replace the faces of a square tiling (quadrille). It is also called the Union Jack lattice because of the resemblance to the UK flag of the triangles surrounding its degree-8 vertices. It is labeled V4.8.8 because each isosceles triangle face has two types of vertices: one with 4 triangles, and two with 8 triangles. As a dual uniform tiling It is the dual tessellation of the tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Uniform Tilings
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type of irregular face. John Conway called these uniform duals ''Catalan tilings'', in parallel to the Catalan solid polyhedra. Uniform tilings are listed by their vertex configuration, the sequence of faces that exist on each vertex. For example ''4.8.8'' means one square and two octagons on a vertex. These 11 uniform tilings have 32 different '' uniform colorings''. A uniform coloring allows identical sided polygons at a vertex to be colored differently, while still maintaining vertex-uniformity and transformational congruence between vertices. (Note: Some of the tiling images shown below are ''not'' color-uniform.) In addition to the 11 convex uniform tilings, there are also 14 known nonconvex tilings, using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Square Tiling
In geometry, the truncated square tiling is a semiregular tiling, semiregular tiling by regular polygons of the Euclidean plane with one square (geometry), square and two octagons on each vertex (geometry), vertex. This is the only edge-to-edge tiling by regular polygon, regular convex polygons which contains an octagon. It has Schläfli symbol of ''t''. John Horton Conway, Conway calls it a truncated quadrille, constructed as a truncation (geometry), truncation operation applied to a square tiling (quadrille). Other names used for this pattern include Mediterranean tiling and octagonal tiling, which is often represented by smaller squares, and nonregular octagons which alternate long and short edges. There are 3 List of regular polytopes#Euclidean tilings, regular and 8 List of uniform tilings, semiregular tilings in the plane. Uniform colorings There are two distinct uniform colorings of a truncated square tiling. (Naming the colors by indices around a vertex (4.8.8): 122, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrangement Of Lines
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the ''cells'' of the arrangement, line segments and rays, the ''edges'' of the arrangement, and points where two or more lines cross, the ''vertices'' of the arrangement. When considered in the projective plane rather than in the Euclidean plane, every two lines cross, and an arrangement is the projective dual to a finite set of points. Arrangements of lines have also been considered in the hyperbolic plane, and generalized to ''pseudolines'', curves that have similar topological properties to lines. The initial study of arrangements has been attributed to an 1826 paper by Jakob Steiner. An arrangement is said to be ''simple'' when at most two lines cross at each vertex, and ''simplicial'' when all cells are triangles (including the unbounded cells, as subsets of the projective plane). There are three kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits. There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells. Hints at a general definition Given an action of a group ''G'' on a topological space ''X'' by homeomorphisms, a fundamental domain for this action is a set ''D'' of representatives for the orbits. It is usually required to be a reasonably nice set topologically, in one of several ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessarily have unit size, or even a particular size at all. Rather, the primitive cell is the closest analogy to a unit vector, since it has a determined size for a given lattice and is the basic building block from which larger cells are constructed. The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell, which is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations. There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point, it is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quilting
Quilting is the process of joining a minimum of three layers of textile, fabric together either through stitching manually using a Sewing needle, needle and yarn, thread, or mechanically with a sewing machine or specialised longarm quilting system. An array of stitches is passed through all layers of the fabric to create a three-dimensional padded surface. The three layers are typically referred to as the top fabric or quilt top, Batting (material), batting or insulating material, and the backing. Quilting varies from a purely functional fabric joinery technique to highly elaborate, decorative three dimensional surface treatments. A wide variety of textile products are traditionally associated with quilting, including bed coverings, home furnishings, garments and costumes, wall hangings, Quilt art, artistic objects, and cultural artifacts. A quilter can employ a wide range of effects that contribute to the quality and utility of the final quilted material. To create these ef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Postal Service
The United States Postal Service (USPS), also known as the Post Office, U.S. Mail, or simply the Postal Service, is an independent agencies of the United States government, independent agency of the executive branch of the federal government of the United States, United States federal government responsible for providing mail, postal service in the United States, its insular areas and Compact of Free Association, associated states. It is one of a few government agencies Postal Clause, explicitly authorized by the Constitution of the United States. As of March 29, 2024, the USPS has 525,377 career employees and nearly 114,623 pre-career employees. The USPS has a monopoly on traditional Letter (message), letter delivery within the U.S. and operates under a Universal service, universal service obligation (USO), both of which are defined across a broad set of legal mandates, which obligate it to provide uniform price and quality across the entirety of its service area. The Post ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Postage Stamp
A postage stamp is a small piece of paper issued by a post office, postal administration, or other authorized vendors to customers who pay postage (the cost involved in moving, insuring, or registering mail). Then the stamp is affixed to the face or address-side of any item of mail—an envelope or other postal cover (e.g., packet, box, mailing cylinder)—which they wish to send. The item is then processed by the postal system, where a postmark or Cancellation (mail), cancellation mark—in modern usage indicating date and point of origin of mailing—is applied to the stamp and its left and right sides to prevent its reuse. Next the item is delivered to its address. Always featuring the name of the issuing nation (with the exception of the Postage stamps and postal history of the United Kingdom, United Kingdom), a denomination of its value, and often an illustration of persons, events, institutions, or natural realities that symbolize the nation's traditions and values, every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hare Games
Hare games are two-player abstract strategy board games that were popular in medieval northern Europe up until the 19th century. In this game, a hare is trying to get past three dogs who are trying to surround it and trap it. The three dogs are represented by three pieces which normally start on one end of the board, and the hare is represented by one piece that usually starts in the middle of the board or is dropped on any vacant point in the beginning of the game. Hare games are similar to Bear games and hunt games. One side has more pieces than the other with the larger side attempting to hem in the smaller side. The smaller side though is usually compensated with more powers. Where hare games differ is that the hounds can only move forward or sideways, and not backwards. The hunters in the Bear games can move in all directions. Furthermore, the dog in the hare games cannot capture any of the hares, unlike the tigers, leopards, jaguars, and foxes in the hunt games which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adugo
Adugo, also known as Jogo da Onça (, ) is a two-player abstract strategy game from the Bororo (Brazil), Bororo tribe in the Pantanal region of Brazil. It is a hunting game similar to those in Southeast Asia and the Indian subcontinent. It is especially similar to komikan, rimau, rimau-rimau, main tapal empat, and bagha-chall as they all use an alquerque-based board. Adugo is specifically a tiger hunt game (or tiger game). Komikan may be the same game as adugo. Komikan is the name given by the Mapuches in Chile. In adugo, the jaguar ("adugo", in Bororo's language) is hunting the dogs ("arikau"). The game is also known as jaguar and dogs. It is thought that the Spanish brought alquerque to the Americas, and this accounts for the use of the alquerque board in this game. Equipment The board used is an expanded alquerque board with one triangular patterned board on one of its sides. There is only one jaguar and 14 dogs. The jaguar is colored black, and the 14 dogs are colored white ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brazil
Brazil, officially the Federative Republic of Brazil, is the largest country in South America. It is the world's List of countries and dependencies by area, fifth-largest country by area and the List of countries and dependencies by population, seventh-largest by population, with over 212 million people. The country is a federation composed of 26 Federative units of Brazil, states and a Federal District (Brazil), Federal District, which hosts the capital, Brasília. List of cities in Brazil by population, Its most populous city is São Paulo, followed by Rio de Janeiro. Brazil has the most Portuguese-speaking countries, Portuguese speakers in the world and is the only country in the Americas where Portuguese language, Portuguese is an Portuguese-speaking world, official language. Bounded by the Atlantic Ocean on the east, Brazil has a Coastline of Brazil, coastline of . Covering roughly half of South America's land area, it Borders of Brazil, borders all other countries and ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fanorona
Fanorona () is a Abstract strategy game, strategy board game for two players. The game is indigenous to Madagascar. Rules Fanorona has three standard versions: Fanoron-Telo, Fanoron-Dimy, and Fanoron-Sivy. The difference between these variants is the size of board. Fanoron-Telo is played on a 3×3 board and the difficulty can be compared to the game of Tic-tac-toe. Fanoron-Dimy is played on a 5×5 board and Fanoron-Sivy is played on a 9×5 board—Sivy being the most popular. The Sivy board consists of lines and intersections that create a grid with 5 rows and 9 columns subdivided diagonally to form part of the tetrakis square tiling of the plane. A line represents the path where a stone can move during the game. There are weak and strong intersections. At a weak intersection, it is only possible to move a stone horizontally and vertically, while on a strong intersection, it is also possible to move a stone diagonally. A stone can only move from one intersection to an adjacent int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
