Euler along with all other mathematicians and physicists erred in assuming that the paper or blackboard on which they demonstrated their geometry had only a two-dimensional surface and was not a substance having an insideness and outsideness. Synergetics is mathematical science. It is pursued only experientially. Professor Percival Bridgman of Harvard discovered that what made possible Einstein's breakthrough was his insistence on treating not only with physically demonstrable facts but also with all the systemically relevant physical facts demonstrably affecting the central measurements. Synergetic mathematics is always concerned with whole systems and not with parts.
Parts are nonexistent independent of systems.
I have to observe that this sheet of paper on which I am writing has substance, an insideness, and a continuous surface rounding at the paper's edges to become the other side of the paper on which I can also write. Experience begins with whole systems. We do not have parts until we have systems. Systems are always four dimensional or more. I next observe that the six toothpicks did give us a very satisfactory visual awareness of the tetrahedron without any faces.