Dihedral Symmetry Domains 5
Dihedral or polyhedral may refer to: * Dihedral angle, the angle between two mathematical planes * Dihedral (aeronautics), the upward angle of a fixed-wing aircraft's wings where they meet at the fuselage, dihedral ''effect'' of an aircraft, longitudinal dihedral angle of a fixed-wing aircraft * Dihedral group, the group of symmetries of the ''n''-sided polygon in abstract algebra ** Also Dihedral symmetry in three dimensions * Dihedral kite, also known as a bowed kite * Dihedral doors, also known as butterfly doors * Dihedral prime, also known as a dihedral calculator prime * In rock climbing, an inside corner of rock See also * Anhedral (other) * Euhedral, a crystal structure * Polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on th ...

Dihedral Angle
A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called wings) are upwardly inclined to the lateral axis. When downwardly inclined they are said to be at a negative dihedral angle. Mathematical background When the two intersecting planes are described in terms of Cartesian coordinates by the two equations : a_1 x + b_1 y + c_1 z + d_1 = 0 :a_2 x + b_2 y + c_2 z + d_2 = 0 the dihedral angle, \varphi between them is given by: :\cos \varphi = \frac and satisfies 0\le \varphi \le \pi/2. Alternatively, if an ...
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Dihedral (aeronautics)
In aeronautics, dihedral is the angle between the left and right wings (or tail surfaces) of an aircraft. "Dihedral" is also used to describe the effect of sideslip on the rolling of the aircraft. Dihedral angle is the upward angle from horizontal of the wings or tailplane of a fixed-wing aircraft. "Anhedral angle" is the name given to negative dihedral angle, that is, when there is a ''downward'' angle from horizontal of the wings or tailplane of a fixed-wing aircraft. Dihedral angle has a strong influence on dihedral effect, which is named after it. Dihedral effect is the amount of roll moment produced in proportion to the amount of sideslip. Dihedral effect is a critical factor in the stability of an aircraft about the roll axis (the spiral mode). It is also pertinent to the nature of an aircraft's Dutch roll oscillation and to maneuverability about the roll axis. Longitudinal dihedral is a comparatively obscure term related to the pitch axis of an airplane. It ...
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Dihedral Group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, or refers to the symmetries of the -gon, a group of order . In abstract algebra, refers to this same dihedral group. This article uses the geometric convention, . Definition Elements A regular polygon with n sides has 2n different symmetries: n rotational symmetries and n reflection symmetries. Usually, we take n \ge 3 here. The associated rotations and reflections make up the dihedral group \mathrm_n. If n is odd, each axis of symmetry connects the midpoint of one side to the opposite vertex. If n is even, there are n/2 axes of symmetry connecting the midpoints of opposite sides and n/2 axes of symmetry connecting oppo ...
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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 symmetr ...
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Bowed Kite
Bowed kites such as the Japanese rokkaku, and traditional versions of the more familiar "diamond" shaped kites such as the Malay or Eddy, are tensioned into a bow in order to improve their stability to the point where a tail often becomes unnecessary. The classic long-tail diamond kite, with a simple two-point bridle, has its lateral roll or flutter (oscillation) greatly reduced or eliminated by a bow in its horizontal spar. Some modern designs use a fixed plastic joiner with a dihedral shape instead of a bowed spar to achieve the same stability effect. See also * Tetrahedral kite A tetrahedral kite is a multicelled rigid box kite composed of tetrahedrally shaped cells to create a kind of tetrahedral truss. The cells are usually arranged in such a way that the entire kite is also a regular tetrahedron. The kite can be desc ... References Bowed kites at the Virtual Kite Zoo. External linksKite IndexLink Directory, For All Kite Related Websites.* {{Kites Kites ...
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Butterfly Doors
Butterfly doors are a type of car door sometimes seen on high-performance cars. They are slightly different from scissor doors. While scissor doors move straight up via hinge points at the bottom of a car's A-pillar, butterfly doors move up and out via hinges along the A-pillar. This makes for easier entry and exit, at the expense of requiring more clearance than needed for scissor doors. Instances Butterfly doors were first seen in the Alfa Romeo 33 Stradale of 1967.This Is the Vintage Alfa Romeo That Inspired the New 8CThis Is the Vintage Alfa Romeo That Inspired the New 8C accessdate: 15. June 2019 These doors were commonly used in Group C and IMSA GTP prototypes, as they preserved the aerodynamic shape of the canopy while allowing the driver to enter and exit the car more quickly than conventional and gullwing doors. The Toyota Sera, made between 1990 and 1995, was a limited-release car designed exclusively for the Japanese market and the first mass-produced vehicle w ...
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Dihedral Prime
A dihedral prime or dihedral calculator prime is a prime number that still reads like itself or another prime number when read in a seven-segment display, regardless of orientation (normally or upside down), and surface (actual display or reflection on a mirror). The first few decimal dihedral primes are : 2, 5, 11, 101, 181, 1181, 1811, 18181, 108881, 110881, 118081, 120121, 121021, 121151, 150151, 151051, 151121, 180181, 180811, 181081 . The smallest dihedral prime that reads differently with each orientation and surface combination is 120121 which becomes 121021 (upside down), 151051 (mirrored), and 150151 (both upside down and mirrored). The digits 0, 1 and 8 remain the same regardless of orientation or surface (the fact that 1 moves from the right to the left of the seven-segment cell when reversed is ignored). 2 and 5 remain the same when viewed upside down, and turn into each other when reflected in a mirror. In the display of a calculator that can handle hexadecimal ...
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Glossary Of Climbing Terms
__NOTOC__ This glossary of climbing terms is a list of definitions of terms and jargon related to rock climbing and mountaineering. The specific terms used can vary considerably between different English-speaking countries; many of the phrases described here are particular to the United States and the United Kingdom. A B Completing the climb upon one's first attempt ever. Often confused with 'flashing' which is the first attempt of the day. There is a second opportunity for a climber to 'blitz' a wall after 12 months. C D E ...
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Anhedral (other)
Anhedral may refer to: * Anhedral angle, the downward angle from horizontal of the wings or tailplane of a fixed-wing aircraft * Anhedral (petrology) Euhedral crystals (also known as idiomorphic or automorphic crystals) are those that are well-formed, with sharp, easily recognised faces. The opposite is anhedral (also known as ''xenomorphic'' or ''allotriomorphic''): a rock with an anhedral ...

Euhedral
Euhedral crystals (also known as idiomorphic or automorphic crystals) are those that are well-formed, with sharp, easily recognised faces. The opposite is anhedral (also known as ''xenomorphic'' or ''allotriomorphic''): a rock with an anhedral texture is composed of mineral grains that have no well-formed crystal faces or cross-section shape in thin section. Anhedral crystal growth occurs in a competitive environment with no free space for the formation of crystal faces. An intermediate texture with some crystal face-formation is termed subhedral. Crystals that grow from cooling liquid magma typically do not form smooth faces or sharp crystal outlines. As magma cools, the crystals grow and eventually touch each other, preventing crystal faces from forming properly or at all. When snowflakes crystallize, they do not touch each other. Thus, snowflakes form euhedral, six-sided twinned crystals. In rocks, the presence of euhedral crystals may signify that they formed early in the ...
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