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Infobox for polygons, for example, triangles and squares. Template parameters [Edit template data] This template has custom formatting. Parameter Description Type Status Name of shape name no description Example Square String required Image of shape image no description File suggested Image caption caption no description Content optional Type type General type of this shape Content optional ...
An example of a convex polygon: a regular pentagon. In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1]
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 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.
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 regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number of vertices and edges.
A regular polygon is a planar figure with all edges equal and all corners equal. A regular polyhedron is a solid (convex) figure with all faces being congruent regular polygons, the same number arranged all alike around each vertex.
In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces ¯, (,) in quantum cohomology. [ 1 ] : §1 [ 2 ] [ 3 ] These moduli spaces are smooth orbifolds whenever the target space is convex.
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