Zonogon

In geometry, a zonogon is a centrally-symmetric, convex polygon.

[1] Equivalently, it is a convex polygon whose sides can be grouped into parallel pairs with equal lengths and opposite orientations, the two-dimensional analog of a zonohedron.

A regular polygon is a zonogon if and only if it has an even number of sides.

The four-sided zonogons are the square, the rectangles, the rhombi, and the parallelograms.

In this tiling, there is a parallelogram for each pair of slopes of sides in the

[5] For instance, the regular octagon can be tiled by two squares and four 45° rhombi.

[6] In a generalization of Monsky's theorem, Paul Monsky (1990) proved that no zonogon has an equidissection into an odd number of equal-area triangles.

[9] Zonogons are the two-dimensional analogues of three-dimensional zonohedra and higher-dimensional zonotopes.

As such, each zonogon can be generated as the Minkowski sum of a collection of line segments in the plane.

Additionally, every planar cross-section through the center of a centrally-symmetric polyhedron (such as a zonohedron) is a zonogon.