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A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

A superegg is a solid described by the equation |sqrt((x^2+y^2)/(a^2))|^n+|z/b|^n=1. (1) The special case n=2 gives a spheroid. Special cases of volume V_n are given by V_1 = ...

The superellipsoid is a generalization of the ellipsoid by allowing different exponents of the variables in the algebraic representation. It is similarly a generalization of ...

There are two curves commonly known as the Lamé curve: the ellipse evolute and the superellipse.

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

By analogy with the squircle, a term first apparently used by Fernández Guasti et al. (2005), the term "rectellipse" (used here for the first time) is a natural ...

In two dimensions, the curve known as an "egg' is an oval with one end more pointed than the other.

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m<2. If n/m>2, the curve is a hyperellipse.

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...