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  2. Constructible polygon - Wikipedia

    en.wikipedia.org/wiki/Constructible_polygon

    In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinitely many constructible polygons, but only 31 with an odd number of sides are known.

  3. Polygon - Wikipedia

    en.wikipedia.org/wiki/Polygon

    Simple: the boundary of the polygon does not cross itself. 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.

  4. List of polygons - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons

    Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle , quadrilateral and nonagon are exceptions, although the regular forms trigon , tetragon , and enneagon are sometimes encountered as well.

  5. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [20]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.

  6. Simple polygon - Wikipedia

    en.wikipedia.org/wiki/Simple_polygon

    Two simple polygons (green and blue) and a self-intersecting polygon (red, in the lower right, not simple) 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 ...

  7. Rectilinear polygon - Wikipedia

    en.wikipedia.org/wiki/Rectilinear_polygon

    A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons. In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates ...

  8. Pick's theorem - Wikipedia

    en.wikipedia.org/wiki/Pick's_theorem

    Farey sunburst of order 6, with 1 interior (red) and 96 boundary (green) points giving an area of 1 + ⁠ 96 / 2 ⁠ − 1 = 48 [1]. In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary.

  9. Convex polygon - Wikipedia

    en.wikipedia.org/wiki/Convex_polygon

    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]

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