Summary

These are the quadric (or quadratic) surfaces modeled as solids. They are the double cone, the hyperboloids of one and two sheets, the ellipsoid, and the hyperbolic paraboloid. The hyperboloid of two sheets is disconnected, so there's a cylinder joining them. The double cone has two halves meeting at a point, so that region is thickened. The paraboloid and the ellipsoid have bases so they stand upright and don't roll or tip over.