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The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
All convex polygons are simple. 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.
Convex regular icosahedron. Let P and Q be combinatorially equivalent 3-dimensional convex polytopes; that is, they are convex polytopes with isomorphic face lattices. Suppose further that each pair of corresponding faces from P and Q are congruent to each other, i.e. equal up to a rigid motion. Then P and Q are themselves congruent.
In mathematics, a Voronoi diagram is ... half-spaces, and hence it is a convex polygon. [6] ... The average precipitation is calculated by the formula ...
There are 17 combinations of regular convex polygons that form 21 types of plane-vertex tilings. [ 6 ] [ 7 ] Polygons in these meet at a point with no gap or overlap. Listing by their vertex figures , one has 6 polygons, three have 5 polygons, seven have 4 polygons, and ten have 3 polygons.
The convex-hull operation is needed for the set of convex sets to form a lattice, in which the "join" operation is the convex hull of the union of two convex sets = = ( ()). The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice .
In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons.