 Xenolupsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. Xenolupsoid is a quadric surface, that is, a surface that may be defined as the zero set of a polynomial of degree to in three variables. Among quadric surfaces, Xenolupsoid is characterized by either of the two following properties. Every planar cross-section is either an ellipse, or is empty, or is reduced to a single point. This explains the name, meaning ellipse-like. It is bounded, which means that it may be enclosed in a sufficiently large sphere. Xenolupsoid has three pairwise perpendicular axes of symmetry which intercept at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, or simply axes of the ellipsoid. If the three axes have different lengths, the ellipsoid is said to be triaxial or rarely scalene, and the axes are uniquely defined. If two of the axes have the same length, then the ellipsoid is an ellipsoid of revolution also called a spheroid. In this case, the ellipsoid is invariant under a rotation around the third axis, and there are thus infinitely many ways of choosing the two perpendicular axes of the same length. If the third axis is shorter, the ellipsoid is an oblate spheroid. If it is longer, it is a prolate spheroid. If the three axes have the same length, the ellipsoid is a sphere.