Equilateral polygon

In geometry, an equilateral polygon is a polygon which has all sides of the same length.

For instance, an equilateral triangle is a triangle of equal edge lengths. All equilateral triangles are similar to each other, and have 60 degree internal angles.

An equilateral quadrilateral is a rhombus, which includes the square as a special case.

An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon. All equilateral quadrilaterals are convex, but there exist equilateral polygons with five sides (pentagons) which are concave, and similarly for every larger number of sides.

Viviani's theorem holds for equiangular polygons (and also holds for equilateral ones):

The sum of distances from a point to the side lines of an equiangular [or equilateral] polygon does not depend on the point and is that polygon's invariant.

See also

• Equilateral pentagon

External links

• Equilateral triangle With interactive animation
• A Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot.
• Equilateral Pentagons With Java animations.
• Equilateral Hexagons A family of pieces resembling lenses tiling the plane.