# Astroidal Ellipsoid

- Author:
- Simona Riva

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
.

*View*to change the point of view of the surface (or use the predefined gestures on mobile devices).Explore the intersections of the hyperbolic octahedron with planes parallel to the axes