Equilateral polygon with 60° internal angles. An equilateral quadrilateral is called a rhombus, an isotoxal polygon described by an angle α. It includes the square as a special case. A convex equilateral pentagon can be described by two angles α and β, which together determine the other angles. Concave equilateral pentagons exist, as do concave equilateral polygons with any larger number of sides. An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon (a polygon that is both equilateral and equiangular). A tangential polygon (one that has an incircle tangent to all its sides) is equilateral
Equilateral dimension equilateral dimension is the maximum number of disjoint translates that can all touch each other. For a normed vector space of dimension "d", the equilateral dimension is at most 2; that is, the L norm has the highest equilateral dimension among all normed spaces. asked whether every normed vector space of dimension "d" has equilateral dimension at least , but this remains unknown. There exist normed spaces in any dimension for which certain sets of four equilateral points cannot be extended to any larger equilateral set but these spaces may have larger equilateral sets that do not include these four