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An example of a concave polygon. A simple polygon that is not convex is called concave, [1] non-convex [2] or reentrant. [3] A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. [4]
A rectilinear polygon has corners of two types: corners in which the smaller angle (90°) is interior to the polygon are called convex and corners in which the larger angle (270°) is interior are called concave. [1] A knob is an edge whose two endpoints are convex corners. An antiknob is an edge whose two endpoints are concave corners. [1]
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
Concave: Non-convex and simple. There is at least one interior angle greater than 180°. Star-shaped: the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped. Self-intersecting: the boundary of the polygon crosses itself.
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
The external angle is positive at a convex vertex or negative at a concave vertex. For every simple polygon, the sum of the external angles is 2 π {\displaystyle 2\pi } (one full turn, 360°). Thus the sum of the internal angles, for a simple polygon with n {\displaystyle n} sides is ( n − 2 ) π {\displaystyle (n-2)\pi } .
The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
In a concave quadrilateral, one interior angle is bigger than 180°, and one of the two diagonals lies outside the quadrilateral. A dart (or arrowhead) is a concave quadrilateral with bilateral symmetry like a kite, but where one interior angle is reflex.