Given our small room dimensions, picking a cell at a room surface, edge, or corner is rather common — the region of a cell is likely to be smaller than the maximum 27-elements of a 3x3x3 subsection.

But what we can say based on what we're picking up on the surface it looks like it is more.

Picking up the height info of the three dimensional surface from two dimensional plane based on the arithmetics hereinbefore, and reconstructing the three dimensional surface.