Definition of impossible objects

Let the sets F₂ and G₃ of the two- and three-dimensional objects be given, as well as the reconstruction of the third dimension,

K_2,3: F₂ —› G₃

Then a twodimensional object f in F₂ is an impossible object, if

K_2,3(f) is not in G₃,

i.e., if there exists no three-dimensional object which, being projected on the plane, yields the figure f. Vice versa, a possible object always is a projection of a three-dimensional object.