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Dihedral Symmetry In Three Dimensions
In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as an abstract group is a dihedral group Dih''n'' (for ''n'' ≥ 2). Types There are 3 types of dihedral symmetry in three dimensions, each shown below in 3 notations: Schönflies notation, Coxeter notation, and orbifold notation. ;Chiral: *''Dn'', 'n'',2sup>+, (22''n'') of order 2''n'' – dihedral symmetry or para-n-gonal group (abstract group: ''Dihn''). ;Achiral: *''Dnh'', 'n'',2 (*22''n'') of order 4''n'' – prismatic symmetry or full ortho-n-gonal group (abstract group: ''Dihn'' × ''Z''2). *''Dnd'' (or ''Dnv''), ''n'',2+ (2*''n'') of order 4''n'' – antiprismatic symmetry or full gyro-n-gonal group (abstract group: ''Dih''2''n''). For a given ''n'', all three have ''n''-fold rotational symmetry about one axis (rotation by an angle of 360°/''n'' does not change the object), and 2-fold rotational symmet ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antiprism
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are triangles, rather than quadrilaterals. The dual polyhedron of an -gonal antiprism is an -gonal trapezohedron. History At the intersection of modern-day graph theory and coding theory, the triangulation of a set of points have interested mathematicians since Isaac Newton, who fruitlessly sought a mathematical proof of the kissing number problem in 1694. The existence of antiprisms was discussed, and their name was coined by Johannes Kepler, though it is possible that they were previously known to Archimedes, as they satisfy the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beach Ball
''Beach Ball'' is a 1965 American beach party movie starring Edd Byrnes and partly financed by Roger Corman.Ed. J. Philip di Franco, ''The Movie World of Roger Corman'', Chelsea House Publishers, 1979, p. 145 It features appearances by The Supremes, The Walker Brothers, and The Righteous Brothers. Tom Lisanti called it "arguably the breeziest and most enjoyable ''Beach Party'' clones. It is also the most blatant rip off." Plot Dick Martin manages a rock and roll group, The Wigglers (Bango, Jack and Bob). They are told by music store owner Mr Wolf that the group owes him $1,000 for their instruments and have to raise money. Martin tries to convince Susan, the credit union manager for a local college, Cast *Edd Byrnes as Dick Martin *Chris Noel as Susan * Robert Logan as Bango *Gail Gilmore as Deborah *Aron Kincaid as Jack *Mikki Jamison as Augusta *Don Edmonds as Bob *Brenda Benet as Samantha *Anna Lavelle as Polly *James Wellman as Mr. Wolf *The Supremes (Florence Ballard, Dian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseball
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding team, called the pitcher, throws a ball that a player on the batting team, called the batter, tries to hit with a bat. The objective of the offensive team (batting team) is to hit the ball into the field of play, away from the other team's players, allowing its players to run the bases, having them advance counter-clockwise around four bases to score what are called " runs". The objective of the defensive team (referred to as the fielding team) is to prevent batters from becoming runners, and to prevent runners' advance around the bases. A run is scored when a runner legally advances around the bases in order and touches home plate (the place where the player started as a batter). The principal objective of the batting team is to hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseball (crop)
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding team, called the pitcher, throws a ball that a player on the batting team, called the batter, tries to hit with a bat. The objective of the offensive team (batting team) is to hit the ball into the field of play, away from the other team's players, allowing its players to run the bases, having them advance counter-clockwise around four bases to score what are called " runs". The objective of the defensive team (referred to as the fielding team) is to prevent batters from becoming runners, and to prevent runners' advance around the bases. A run is scored when a runner legally advances around the bases in order and touches home plate (the place where the player started as a batter). The principal objective of the batting team is to have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basketball
Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (approximately in diameter) through the defender's hoop (a basket in diameter mounted high to a Backboard (basketball), backboard at each end of the court, while preventing the opposing team from shooting through their own hoop. A Field goal (basketball), field goal is worth two points, unless made from behind the 3 point line, three-point line, when it is worth three. After a foul, timed play stops and the player fouled or designated to shoot a technical foul is given one, two or three one-point free throws. The team with the most points at the end of the game wins, but if regulation play expires with the score tied, an additional period of play (Overtime (sports), overtime) is mandated. Players advance the ball by bouncing it while walking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basketball
Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (approximately in diameter) through the defender's hoop (a basket in diameter mounted high to a Backboard (basketball), backboard at each end of the court, while preventing the opposing team from shooting through their own hoop. A Field goal (basketball), field goal is worth two points, unless made from behind the 3 point line, three-point line, when it is worth three. After a foul, timed play stops and the player fouled or designated to shoot a technical foul is given one, two or three one-point free throws. The team with the most points at the end of the game wins, but if regulation play expires with the score tied, an additional period of play (Overtime (sports), overtime) is mandated. Players advance the ball by bouncing it while walking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order 4 Dihedral Symmetry Subgroup Tree
Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of different ways * Hierarchy, an arrangement of items that are represented as being "above", "below", or "at the same level as" one another * an action or inaction that must be obeyed, mandated by someone in authority People * Orders (surname) Arts, entertainment, and media * ''Order'' (album), a 2009 album by Maroon * "Order", a 2016 song from '' Brand New Maid'' by Band-Maid * ''Orders'' (1974 film), a 1974 film by Michel Brault * ''Orders'', a 2010 film by Brian Christopher * ''Orders'', a 2017 film by Eric Marsh and Andrew Stasiulis * ''Jed & Order'', a 2022 film by Jedman Business * Blanket order, purchase order to allow multiple delivery dates over a period of time * Money order or postal order, a financial instrument usually inten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order 2 Dihedral Symmetry Subgroup Tree
Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of different ways * Hierarchy, an arrangement of items that are represented as being "above", "below", or "at the same level as" one another * an action or inaction that must be obeyed, mandated by someone in authority People * Orders (surname) Arts, entertainment, and media * ''Order'' (album), a 2009 album by Maroon * "Order", a 2016 song from '' Brand New Maid'' by Band-Maid * ''Orders'' (1974 film), a 1974 film by Michel Brault * ''Orders'', a 2010 film by Brian Christopher * ''Orders'', a 2017 film by Eric Marsh and Andrew Stasiulis * ''Jed & Order'', a 2022 film by Jedman Business * Blanket order, purchase order to allow multiple delivery dates over a period of time * Money order or postal order, a financial instrument usually inten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedral Symmetry
150px, A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation. The group of all (not necessarily orientation preserving) symmetries is isomorphic to the group S4, the symmetric group of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4. Details Chiral and full (or achiral tetrahedral symmetry and pyritohedral symmetry) are discrete point symmetries (or equivalently, symmetries on the sphere). They are among the crystallographic point groups of the cubic crystal system. Seen in stereographic projection the edges of the tetrakis hexahedron form 6 circles (or centrally radial lines) in the plane. E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and anot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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