A dihedral angle is the angle between two intersecting planes or half-planes. It is a plane angle formed on a third plane, perpendicular to the line of intersection between the two planes or the common edge between the two half-planes. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common.
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👉 Dihedral angle in the context of Spherical lune
In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points. It is an example of a digon, {2}θ, with dihedral angle θ. The word "lune" derives from luna, the Latin word for Moon.
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Dihedral angle in the context of Vertex-transitive
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.
Technically, one says that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope acts transitively on its vertices, or that the vertices lie within a single symmetry orbit.
Dihedral angle in the context of Cuboid
In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.
General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram faces. Rhombohedron is a cuboid with six rhombus faces. A square frustum is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by truncating the apex of a square pyramid.In attempting to classify cuboids by their symmetries, Robertson (1983) found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects".
Dihedral angle in the context of Hour angle
In astronomy and celestial navigation, the hour angle is the dihedral angle between the meridian plane (containing Earth's axis and the zenith) and the hour circle (containing Earth's axis and a given point of interest).
It may be given in degrees, time, or rotations depending on the application.The angle may be expressed as negative east of the meridian plane and positive west of the meridian plane, or as positive westward from 0° to 360°. The angle may be measured in degrees or in time, with 24 = 360° exactly.In celestial navigation, the convention is to measure in degrees westward from the prime meridian (Greenwich hour angle, GHA), from the local meridian (local hour angle, LHA) or from the first point of Aries (sidereal hour angle, SHA).
Dihedral angle in the context of Protein secondary structure
Protein secondary structure is the local spatial conformation of the polypeptide backbone excluding the side chains. The two most common secondary structural elements are alpha helices and beta sheets, though beta turns and omega loops occur as well. Secondary structure elements typically spontaneously form as an intermediate before the protein folds into its three dimensional tertiary structure.
Secondary structure is formally defined by the pattern of hydrogen bonds between the amino hydrogen and carboxyl oxygen atoms in the peptide backbone. Secondary structure may alternatively be defined based on the regular pattern of backbone dihedral angles in a particular region of the Ramachandran plot regardless of whether it has the correct hydrogen bonds.