Say that you were to fill space with spheres and inflate them what shape would the bounds make?
We can assume the spheres are packed optimally, just like you would stack cannon balls, what kind of shape would these form?
We already know that the shape tiles 3D space perfectly.
It's a relatively simple question, and i thought it could have been a cubotahedron, but i wanted to make sure and ask you, since i couldnt find a good answer and the cubotahedron doesnt seem to tile space.