# Bowtie

Bowtie Rank2
TypeSemi-uniform
SpaceSpherical
Notation
Bowers style acronymBowtie
Elements
Edges2+2
Vertices4
Measures (edge lengths a [short], b [long])
Circumradius$\frac{b}{2}$ Area0
Angle$\arccos\left(\frac{a}{b}\right)$ Related polytopes
ArmyRect
ConjugateBowtie
Abstract & topological properties
OrientableYes
Properties
SymmetryK2, order 4
ConvexNo
NatureTame

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, ±b2a2/2).

## In vertex figures

Many uniform hemipolyhedra have bowties as their vertex figure.