Superellipsoid

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Superellipsoid
Dimensions2
ConnectedYes
CompactYes
Euler characteristic0
OrientableYes
SymmetryK3, order 8

A superellipsoid is a surface defined as the set of points in 3D space such that where , or any scaling (possibly nonuniform) of such a surface. "Superellipsoid" refers to both the surface and the solid that it encloses. All cross sections of a superellipsoid in planes parallel to the xy-plane are superellipses of exponent , and the cross sections in the xz- and yz-planes are superellipses of exponent .

Superellipsoids come from the field of computer graphics. Special settings produce spheres, Steinmetz solids, bicones, supereggs, and the regular octahedron. If the constants are permitted to tend to infinity, as they often are in computer graphics, cylinders and cuboids can also be produced.