Crossed polygon

A crossed polygon is a polygon in the plane with a turning number or density of zero, with the appearance of a figure 8, infinity symbol, or lemniscate curve.

The vertices with clockwise turning angles equal the vertices with counterclockwise turning angles.

A crossed polygon will always have at least 2 edges or vertices intersecting or coinciding.

Any convex polygon with 4 or more sides can be remade into a crossed polygon by swapping the positions of two adjacent vertices.

Crossed polygons are common as vertex figures of uniform star polyhedra.

A crossed equilateral pentagon
The vertex figure of a snub icosidodecadodecahedron is a crossed hexagon.
A symmetric crossed decagon