Bicone

A bicone, also called a spindle, is a bipyramid based on a disk. As a result it can be formed by attaching two cones at the circular base, leaving only the lateral surfaces of the cones exposed. It is also the solid of revolution of a rhombus around one of its diagonals.

Coordinates
Where r is the radius of the base and h is the height:

The vertices of a bicone are


 * $$\left(0,\,0,\,±h\right).$$

Points on the edge of a bicone are all points (x,y,0) such that


 * $$x^2+y^2=r^2.$$

Points on the surface of a bicone are all points (x,y,z) such that


 * $$\sqrt{x^2+y^2} = r(h-|z|).$$

Points in the interior of a bicone are all points (x,y,z) such that
 * $$\sqrt{x^2+y^2} < r(h-|z|).$$