Turning a penrose triangle inside out

Why do impossible figures, which cannot exist in three dimensions, appear to make threedimensional sense? In order to shed some light on this question the limits may be tested to which three-dimensional operations on these figures can be performed. In this paper a particularly difficult operation, viz., torus eversion is attempted. Not only is an eversion found to be possible but an unfamiliar impossibility develops. The regular form of the eversion is shown to be unique.