What is the interpenetrative sphere?

Besides the line, square and cube, there is something, which represents what we might call the interpenetrative sphere. 

We have motion forward, upward, across, but in the future, there will also be motion through. At present, one body has to move out of the way of another, but then they will just interpenetrate. To understand this more easily, think of the simile used of the man who could only walk in two dimensions.

You can walk in three, but in the future, there will be four—

Up—

Down—

Across—

Through.

I think a symbol to be added to the line, square and cube might be this—

A hollow sphere, with other hollow and smaller spheres enclosed within it, something like the balls within balls cut by the Chinese.