Rectangle

Rectangle
(OFF file)
Rank	2
Type	Semi-uniform
Space	Spherical
Notation
Bowers style acronym	Rect
Coxeter diagram	x y
Elements
Edges	2+2
Vertices	4
Vertex figure	Dyad
Measures (edge lengths a, b)
Circumradius	$\frac{\sqrt{a^2+b^2}}{2}$
Area	$ab$
Angle	90°
Central density	1
Related polytopes
Army	Rect
Dual	Rhombus
Conjugate	Rectangle
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	K2, order 4
Convex	Yes
Nature	Tame

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
Dodecadodecahedron		(1+√5)/2, (√5–1)/2

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".

• Klitzing, Richard. "Polygons"