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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 Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8]
Convex and concave kites. A kite is a quadrilateral with reflection symmetry across one of its diagonals. Equivalently, it is a quadrilateral whose four sides can be grouped into two pairs of adjacent equal-length sides. [1] [7] A kite can be constructed from the centers and crossing points of any two intersecting circles. [8]
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]
Examples include Circoporus octahedrus, Circogonia icosahedra, Lithocubus geometricus and Circorrhegma dodecahedra; the shapes of these creatures are indicated by their names. [5] The outer protein shells of many viruses form regular polyhedra. For example, HIV is enclosed in a regular icosahedron, as is the head of a typical myovirus. [6] [7]
The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations. Some of the intersecting faces are drawn visually incorrectly because they are not properly intersected visually to show which portions are in front.