Bowtie

The bowtie, or crossed rectangle, is a nonconvex semi-uniform 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 only semi-uniform polygon with an even amount of sides that isn't the truncation of any other polygon. It is also unusual in that its sides with equal length don't go around its circumcircle in a consistent direction. It is the only semi-uniform polygon that does not have a set angle; its angle varies with its proportions.

Bowties are the simplest possible type of hemipolytope.

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, ±$\sqrt{b^{2}–a^{2}}$/2).

In vertex figures
Polyhedra with bowtie vertex figures are known as hemipolyhedra. They all have faces whose planes pass through their center.