Mathematical Experiment 7

Construct this surface which appears like this from various angles:

Construct three mutually tangential cylinders of the same size situated like this:

Arrange three identical mutually tangential cones like this:

Arrange four identical mutually tangential half-cones like this:

Arrange eight identical half-cones each tangent to the other three like this:

Construct the solid bounded by the parabolic cylinder

z = 4 - y2

and the elliptic paraboloid

z = x2 + 3y2.