As 16 = 24 (a power of two), a regular hexadecagon is constructible using compass and straightedge: this was already known to ancient Greek mathematicians.

Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.

[4] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.

The list OEIS: A006245 enumerates the number of solutions as 1232944, including up to 16-fold rotations and chiral forms in reflection.

In 3-dimensions it will be a zig-zag skew hexadecagon and can be seen in the vertices and side edges of an octagonal antiprism with the same D8d, [2+,16] symmetry, order 32.

Deeper truncations of the regular octagon and octagram can produce isogonal (vertex-transitive) intermediate hexadecagram forms with equally spaced vertices and two edge lengths.

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.

[7] An octagonal star can be seen as a concave hexadecagon: The latter one is seen in many architectures from Christian to Islamic, and also in the logo of IRIB TV4.