Astroidal Ellipsoid
The name of this surface comes from the property that its sections with planes parallel to the axes are astroids.
A parameterization of its equation is:
, ,
and the Cartesian equation is
For the special case this surface is named hyperbolic octahedron, and has the following properties:
- it has the same vertices and symmetries of the regular octahedron
- it is the envelope of the planes that intersect the axes at the vertices of a triangle whose distance between the barycenter and the origin is constant, and equal to .
Explore the intersections of the hyperbolic octahedron with planes parallel to the axes