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Triangular Tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ). The triangular tiling can also be called a kishextille by a kis operation that adds a center point and triangles to replace the faces of a hextille. It is one of three regular tilings of the plane. The other two are the square tiling and the hexagonal tiling. Uniform colorings There are 9 distinct uniform colorings of a triangular tiling. (Naming the colors by indices on the 6 triangles around a vertex: 111111, 111112, 111212, 111213, 111222, 112122, 121212, 121213, 121314) Three of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Regular Polytopes
This article lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ''n''-sphere, Euclidean and hyperbolic spaces. A Schläfli symbol describing an ''n''-polytope equivalently describes a tessellation of an (''n'' − 1)-sphere. In addition, the symmetry of a regular polytope or tessellation is expressed as a Coxeter group, which Coxeter expressed identically to the Schläfli symbol, except delimiting by square brackets, a notation that is called Coxeter notation. Another related symbol is the Coxeter-Dynkin diagram which represents a symmetry group with no rings, and the represents regular polytope or tessellation with a ring on the first node. For example, the cube has Schläfli symbol , and with its octahedral symmetry, ,3or , it is represented by Coxeter diagram . The regular polytopes are grouped by dimension and subgrouped by convex, nonconvex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedean Coloring
In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different symmetries can be expressed on the same geometric figure with the faces following different uniform color patterns. A ''uniform coloring'' can be specified by listing the different colors with indices around a vertex figure. n-uniform figures In addition, an ''n''-uniform coloring is a property of a ''uniform figure'' which has ''n'' types vertex figure, that are collectively vertex transitive. Archimedean coloring A related term is ''Archimedean color'' requires one vertex figure coloring repeated in a periodic arrangement. A more general term are ''k''-Archimedean colorings which count ''k'' distinctly colored vertex figures. For example, this Archimedean coloring (left) of a triangular tiling In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Coloring
In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different symmetries can be expressed on the same geometric figure with the faces following different uniform color patterns. A ''uniform coloring'' can be specified by listing the different colors with indices around a vertex figure. n-uniform figures In addition, an ''n''-uniform coloring is a property of a ''uniform figure'' which has ''n'' types vertex figure, that are collectively vertex transitive. Archimedean coloring A related term is ''Archimedean color'' requires one vertex figure coloring repeated in a periodic arrangement. A more general term are ''k''-Archimedean colorings which count ''k'' distinctly colored vertex figures. For example, this Archimedean coloring (left) of a triangular tiling In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 111112
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 121213
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 111212
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 121314
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 111222
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Triangular Tiling 111213
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates in prisons. In some countries, some other officials also wear uniforms in their duties; such is the case of the Commissioned Corps of the United States Public Health Service or the French prefects. For some organizations, such as police, it may be illegal for non members to wear the uniform. Etymology From the Latin ''unus'', one, and ''forma'', form. Corporate and work uniforms Workers sometimes wear uniforms or corporate clothing of one nature or another. Workers required to wear a uniform may include retail workers, bank and post-office workers, public-security and health-care workers, blue-collar employees, personal trainers in health clubs, instructors in summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound 3 Triangular Tilings
Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive structures * Compound (migrant labour), a hostel for migrant workers such as those historically connected with mines in South Africa * The Compound, an area of Palm Bay, Florida, US * Komboni or compound, a type of slum in Zambia Government and law * Composition (fine), a legal procedure in use after the English Civil War ** Committee for Compounding with Delinquents, an English Civil War institution that allowed Parliament to compound the estates of Royalists * Compounding treason, an offence under the common law of England * Compounding a felony, a previous offense under the common law of England Linguistics * Compound (linguistics), a word that consists of more than one radical element * Compound sentence (linguistics), a type of sente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
