|
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 truncated ... [...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 calls 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 star ... [...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 music, an arrangement is a musical adaptation of an existing composition. Differences from the original composition may include reharmonization, melodic paraphrasing, orchestration, or formal development. Arranging differs from orchestration in that the latter process is limited to the assignment of notes to instruments for performance by an orchestra, concert band, or other musical ensemble. Arranging "involves adding compositional techniques, such as new thematic material for introductions, transitions, or modulations, and endings. Arranging is the art of giving an existing melody musical variety".(Corozine 2002, p. 3) In jazz, a memorized (unwritten) arrangement of a new or pre-existing composition is known as a ''head arrangement''. Classical music Arrangement and transcriptions of classical and serious music go back to the early history of this genre. Eighteenth century J.S. Bach frequently made arrangements of his own and other composers' pieces. ... [...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 preci ... [...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 term given to the process of joining a minimum of three layers of fabric together either through stitching manually using a needle and 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 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 that includes bed coverings, soft home furnishings, garments and costumes, wall hangings, artistic objects and cultural artefacts. A wide range of effects can be employed by the quilter that contribute to the final surface quality and utility of the quilted material. The quilter controls these effect ... [...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 Postal Service, is an independent agency of the executive branch of the United States federal government responsible for providing postal service in the U.S., including its insular areas and associated states. It is one of the few government agencies explicitly authorized by the U.S. Constitution. The USPS, as of 2021, has 516,636 career employees and 136,531 non-career employees. The USPS traces its roots to 1775 during the Second Continental Congress, when Benjamin Franklin was appointed the first postmaster general; he also served a similar position for the colonies of the Kingdom of Great Britain. The Post Office Department was created in 1792 with the passage of the Postal Service Act. It was elevated to a cabinet-level department in 1872, and was transformed by the Postal Reorganization Act of 1970 into the U.S. Postal Service as an independent agency. Since the early 1980s, m ... [...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), who then affix the stamp to the face or address-side of any item of mail—an envelope or other postal cover (e.g., packet, box, mailing cylinder)—that they wish to send. The item is then processed by the postal system, where a postmark or 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. The item is then delivered to its addressee. Always featuring the name of the issuing nation (with the exception of the 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 stamp is printed on a piece of usually rectangular, but sometimes triangular ... [...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 can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adugo
Adugo is a two-player abstract strategy game from the 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. The jaguar (Panthera onca) is called "onça". The dogs are called "cachorro". 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brazil
Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area and the seventh most populous. Its capital is Brasília, and its most populous city is São Paulo. The federation is composed of the union of the 26 States of Brazil, states and the Federal District (Brazil), Federal District. It is the largest country to have Portuguese language, Portuguese as an List of territorial entities where Portuguese is an official language, official language and the only one in the Americas; one of the most Multiculturalism, multicultural and ethnically diverse nations, due to over a century of mass Immigration to Brazil, immigration from around the world; and the most populous Catholic Church by country, Roman Catholic-majority country. Bounded by the Atlantic Ocean on the east, Brazil has a Coastline of Brazi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fanorona
Fanorona () is a strategy board game for two players. The game is indigenous to Madagascar. Rules Fanorona has three standard versions: Fanoron-Telo, Fanoron-Dimy, and Fanoron-Tsivy. The difference between these variants is the size of board played on. Fanoron-Telo is played on a 3×3 board and the difficulty of this game can be compared to the game of tic-tac-toe. Fanoron-Dimy is played on a 5×5 board and Fanoron-Tsivy is played on a 9×5 board—Tsivy being the most popular. The Tsivy 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 along which 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 adjace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Brazil")
