It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions. It is also named "spherical cone" because its intersections with hyperplanes perpendicular to the w-axis are spheres.
It is a quartic surface, and one of the possible 3-manifolds that are four-dimensional counterparts to conical surfaces in three dimensions. It is also referred to as a "spherical cone" because its intersections with hyperplanes perpendicular to the w-axis form spheres.