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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.
The following method of construction uses Carlyle circles, as shown below. Based on the construction of the regular 17-gon, one can readily construct n -gons with n being the product of 17 with 3 or 5 (or both) and any power of 2: a regular 51-gon, 85-gon or 255-gon and any regular n -gon with 2 h times as many sides.
For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already constructed foci and major axis (think two pins and a piece of string) is just ...
For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}. If m is 2, for example, then every second point is joined. If m is 3, then every third point is joined. The boundary of the polygon winds around the center m times. The (non-degenerate) regular stars of up to 12 ...
A wide variety of 3D graphics software packages are available for use in constructing polygon meshes. One of the more popular methods of constructing meshes is box modeling, which uses two simple tools: The subdivide tool splits faces and edges into smaller pieces by adding new vertices. For example, a square would be subdivided by adding one ...
One method to construct a regular pentagon in a given circle is described by Richmond [3] and further discussed in Cromwell's Polyhedra. [4] The top panel shows the construction used in Richmond's method to create the side of the inscribed pentagon. The circle defining the pentagon has unit radius.
With a construction system that can trisect angles, such as mathematical origami, more numbers of sides are possible, using Pierpont primes in place of Fermat primes, including -gons for equal to 7, 13, 14, 17, 19, etc. [6] Geometric Origami provides explicit folding instructions for 15 different regular polygons, including those with 3, 5, 6 ...
The shrinking process, the straight skeleton (blue) and the roof model. In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton.It is similar in some ways to the medial axis but differs in that the skeleton is composed of straight line segments, while the medial axis of a polygon may involve parabolic curves.