 Aristotle agrees that atoms could fill space if they were all cubes. Pressing his luck, Aristotle goes on to claim that tetrahedra can also complete space. It is testament to Aristotle’s subsequent authority that this claim was accepted for seventeen hundred years—despite being easily refutable by anyone trying to snugly combine tetrahedral blocks. Almost any choice of shapes guarantees interstitial vacua. This geometrical pressure for tiny vacua creates a precedent for the cosmic void (which surrounds the material cosmos) and the intermediate empty spaces that provide a promising explanation of how motion is possible.