In 1910 Steinitz published the very influential paper Algebraische Theorie der Körper (German: Algebraic Theory of Fields, Crelle's Journal (1910), 167–309). In this paper he axiomatically studies the properties of fields and defines important concepts like prime field, perfect field and the transcendence degree of an field extension. Steinitz also made fundamental contributions to the theory of polyhedra: Steinitz's theorem for polyhedra is that the 1-skeletons of convex polyhedra are exactly the 3-connected planar graphs. His work in this area was published posthumously as a 1934 book, Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie, by Hans Rademacher.