Vertex angle

In geometry, a vertex angle is an angle associated with a vertex of an n-dimensional polytope. Often a vertex angle of a polygon is referred to simply as an angle of the polygon.[1]

A triangle, with interior vertex angles a, b, and c along with exterior angle d

In higher-dimensional polyhedra and polytopes, a vertex angle is an angle formed by two edges of the polyhedron that both belong to a common two-dimensional face of the polyhedron. That is, it is a vertex angle of one of the polygons that form the polyhedron.

Properties

A vertex angle in a polygon is often measured on the interior side of the vertex. For any simple n-gon, the sum of the interior angles is π(n  2) radians or 180(n  2) degrees.[2]

Because more than two lines in a polytope can intersect in the same space, the number of vertex angles from any given vertex is not always one. Because of this, it is sometimes necessary to specify not only the vertex, but also the specific line segments that make up the angle.[3]

gollark: If someone gets access to a computer in my *brain*, they can alter my beliefs and perceptions - subject me to horrible torture forever, make me an entirely different person, sort of thing.
gollark: Currently, if someone gets unauthorized access to my computer, at worst they will have access to a bunch of personal information and passwords, but I can change the passwords and wipe the computer, although it would be somewhat tedious.
gollark: OLEDs still use polarizers except the shiny new Samsung stuff.
gollark: E-ink is kind of bad and expensive, same for CRTs, and micro-LED isn't there yet.
gollark: But then I can't use a computer.

See also

References


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.