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 formula_3 the regular hexadecagon fills approximately 97.45% of its circumcircle.
Dissection.
Coxeter states that every parallel-sided 2"m"-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. The list A006245 enumerates the number of solutions as 1232944, including up to 16-fold rotations and chiral forms in reflection.
Skew hexadecagon.
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.
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: