Hexadecagon

An hexadecagon or hexakaidecagon is a shape with 16 sides and 16 corners.

 Regular hexadecagon 
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}.

 Area 
The area of a regular hexadecagon with edge length t is

Because the hexadecagon has a number of sides that is a power of two, its area can be computed in terms of the circumradius R by truncating Viète's formula:

Since the area of the circumcircle is  the regular hexadecagon fills approximately 97.45% of its circumcircle.

 Dissection
Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/2 rhombs. For the regular hexadecagon, m=8, and it can be divided into 28: 4 squares and 3 sets of 8 rhombs. This decomposition is based on a Petrie polygon projection of a 8-cube, with 28 of 1792 faces. Coxeter, Mathematical recreations and Essays, Thirteenth edition, p.141 The list A006245 enumerates the number of solutions as 1232944, including up to 16-fold rotations and chiral forms in reflection.
+ Dissection into 28 rhombs160px160px

 Skew hexadecagon 
+ 3 regular skew zig-zag hexadecagon{8}#{ } {  }#{ } {  }#{ }120px80px120pxA regular skew hexadecagon is seen as zig-zagging edges of a octagonal antiprism, a octagrammic antiprism, and a octagrammic crossed-antiprism.
A skew hexadecagon is a skew polygon with 24 vertices and edges but not existing on the same plane. The interior of such an hexadecagon is not generally defined. A skew zig-zag hexadecagon has vertices alternating between two parallel planes.

A regular skew hexadecagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew hexadecagon and can be seen in the vertices and side edges of a octagonal antiprism with the same D8d, [2+,16] symmetry, order 32. The octagrammic antiprism, s{2,16/3} and octagrammic crossed-antiprism, s{2,16/5} also have regular skew octagons.

In art
In the early 16th century, Raphael was the first to construct a perspective image of a regular hexadecagon: the tower in his painting The Marriage of the Virgin has 16 sides, elaborating on an eight-sided tower in a previous painting by Pietro Perugino.. Originally published in Nexus III: Architecture and Mathematics, Kim Williams, ed. (Ospedaletto, Pisa: Pacini Editore, 2000), pp. 147–156.

Hexadecagrams (16-sided star polygons) are included in the Girih patterns in the Alhambra..

 Irregular hexadecagons 
An octagonal star can be seen as a concave hexadecagon:
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References

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