Name for the volume "inside" a torus?

Question

If you have a standard ring torus, what's the name for the shape created by the empty space in the middle of the ring with the height equal to the height of the torus? For another explanation, it would be the resultant figure if you took a cube with height $h$, a cylinder with the diameter equal to $h$ and height equal to the circumference of a circle inscribed into one of the faces of the cube, and wrapped the cylinder around the cube such that the two faces of the cylinder touched. I apologize for the potentially confusing explanation, but any help is appreciated.

EDIT: the planar figure to be rotated is basically this

EDIT AGAIN: I believe the jelly donut metaphor is accurate, though I couldn't find any reference elsewhere to "interior of solid torus"

Another Edit: After some more research, I have determined that it is possible a concave cylinder may appropriately describe it, but I'm not sure if it is plagued by the same issue as the hyperboloid (that is, the curves technically cannot perfectly fit the inside of a torus). Is this correct?

Answer 1

Interior of a solid torus sounds fine to me.

To address the edit: call it the jelly.

Answer 2

Since it's the difference between the convex hull and the shape itself, I guess you could call it the convex filling.

Relatively appropriate for a doughnut.

Answer 3

This isn't a name, but it is a slightly more precise description of the shape you're asking for: it's the region described (in cylindrical coordinates) by an equation of the form $$r \le a - \sqrt{b^2-z^2}$$ where $a$ is greater than $b$. In this formulation, $b$ is the inner radius of the torus's circular cross-sections, and $a$ is the distance from the centers of those cross-sections to the axis of symmetry. As Lubin mentioned in the comments under the OP, it resembles a pulley shape. See the graph below.