# Rectangle

Rectangle
Rank2
TypeSemi-uniform
SpaceSpherical
Notation
Bowers style acronymRect
Coxeter diagramx y
Elements
Edges2+2
Vertices4
Measures (edge lengths a, b)
Circumradius${\displaystyle \frac{\sqrt{a^2+b^2}}{2}}$
Area${\displaystyle ab}$
Angle90°
Central density1
Related polytopes
ArmyRect
DualRhombus
ConjugateRectangle
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryK2, order 4
ConvexYes
NatureTame

The rectangle is a semi-uniform quadrilateral with 2 pairs of opposite parallel sides. All interior angles of a rectangle measure 90°. A rectangle is the prism product of two dyads of different lengths.

Any rectangle can tile the euclidean plane, regardless of its sides.

## Vertex coordinates

Coordinates for the vertices of a rectangle with side lengths a and b, centered at the origin, are:

• a/2, ±b/2).

## In vertex figures

Because the rectangle is a semi-uniform polygon, all polyhedra with rectangular vertex figures are quasiregular. They are also all the result of rectification of regular polyhedra.

Rectangles in vertex figures
Name Picture Edge lengths
Tetratetrahedron
1, 1
Cuboctahedron
1, 2
Icosidodecahedron
1, (1+5)/2
Great icosidodecahedron
1, (5–1)/2