Bowtie

The bowtie, or crossed rectangle, is a nonconvex semiuniform quadrilateral with the same vertices as a rectangle but with two of the original sides removed and with the original's diagonals in place instead.

It is the simplest example of a non-orientable polytope.

Vertex coordinates
Coordinates for the vertices of a bowtie with two sides of length a and two intersecting sides of length b, with b > a, are:
 * (±a/2, ±$\sqrt{b^{2}–a^{2}}$).

In vertex figures
Polyhedra with bowtie vertex figures are known as hemipolyhedra.