We can put 4 unit circles inside a square of length 4 units, such that all the circles will touch the boundary and also adjacent circles, and there will be a hollow in between the 4 circles. So we can also consider a 3D cube of length 4 units, and put 8 spheres, where each one will touch the wall, and still be able to put a sphere, at the center of the cube. Now, if we can calculate the volume of the mid-spheres (for 2D -> Circle, for 3D -> Sphere, and from then on, Hypershperes), and we find that at the 9th dimension, the 9D-mid-hypershpere just touches the hyper-cube-walls and in the 10th dimension, the mid-sphere, becomes larger than even the 10 Dimensional cube itself. Now my question, how can these be imagined physically, is there any way out?
Thanks in advance.