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In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. [1] The total sum of the interior angles of a simple decagon is 1440°. Regular decagon
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 ...
However, it is constructible using neusis with use of the angle trisector, [2] or with a marked ruler, [3] as shown in the following two examples. Tetradecagon with given circumcircle : An animation (1 min 47 s) from a neusis construction with radius of circumcircle O A ¯ = 6 {\displaystyle {\overline {OA}}=6} ,
The internal angle at each vertex of a regular dodecagon is 150°. Area The ... The interior of such a dodecagon is not generally defined.
The parametric angle 𝛼 (in degrees or radians) can be chosen to match internal angles of neighboring polygons in a tessellation pattern. In his 1619 work Harmonices Mundi , among periodic tilings, Johannes Kepler includes nonperiodic tilings, like that with three regular pentagons and one regular star pentagon fitting around certain vertices ...
Octadecagon, an exact construction based on the angle trisection 120° by means of the tomahawk, animation 1 min 34 s. The following approximate construction is very similar to that of the enneagon, as an octadecagon can be constructed as a truncated enneagon.
Publication by C. F. Gauss in Intelligenzblatt der allgemeinen Literatur-Zeitung. As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19. [1]
A regular hexadecagon is a hexadecagon in which all angles are equal and all sides are congruent. Its Schläfli symbol is {16} and can be constructed as a truncated octagon, t{8}, and a twice-truncated square tt{4}. A truncated hexadecagon, t{16}, is a triacontadigon, {32}.