where 𝑥 and 𝑦 represent the horizontal and vertical coordinates of points in the rectangular coordinate system, respectively; 𝐴, 𝐵, and 𝑛 are positive real numbers. Superellipses include the circle, the diamond and squares for 𝐴 = 𝐵, and ellipses, rhombi, and rectangles for 𝐴 ≠ 𝐵 for 𝑛 to infinity. Gabriel Lamé introduced these curves to be able to apply geometry to crystals. The absolute values ensure closed curves (Figure ). Interest in superellipses was revived in the 20 th century through the Danish mathematician Piet Hein . The Superformula is a further generalization of superellipses, describing a much wider range of abstract and natural shapes. By transforming supercircles into polar coordinates, the superformula can deal with any symmetry by introducing a symmetry parameter 𝑚. Gielis modeled various ranges of more symmetrical and asymmetrical geometries found in The mathematical expression of the superformula is: