Equilateral polygon Equilateral polygon In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting. All regular polygons and isotoxal polygons are equilateral. An equilateral triangle is a regular triangle
Euclidean tilings by convex regular polygons uniformity which requires edge-to-edge regular polygons. Such isogonal tilings are actually topologically identical to the uniform tilings, with different geometric proportions. Euclidean and general tiling links: Euclidean tilings by convex regular polygons Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler in his "Harmonices Mundi" (Latin: "The Harmony of the World", 1619). Following Grünbaum and Shephard (section 1.3), a tiling is said to be "regular" if the symmetry group of the tiling acts transitively on the "flags" of the tiling, where a flag is a triple consisting