Császár Polyhedron [Note by the Editor]:
During the opening ceremony of the congress, we celebrate the 80th birthday
of Ákos Császár and 55th anniversary of the discovery
of the Császár polyhedron. The latter topic was inspired
by a problem in a mathematical competition for students in 1948: Prove
that there is no polyhedron, beyond the tetrahedron, where any two vertices
are connected by an edge. In other words, the tetrahedron is the only
polyhedron without diagonals. Indeed, this statement is valid for convex
polyhedra. However, Császár gave a concave example that
has no diagonal. Interestingly, his paper of 1949 had no figure, which
is not surprising if we consider the difficulties at Hungarian universities
after World War II. Perhaps, the lack of figures contributed to the fact
that this paper did not inspire many further studies until Donald W. Crowe’s
contributions in the early 1970s and then Martin Gardner’s popular
paper on the “Császár polyhedron” in the Scientific
American (May 1975). Later L. Szilassi and more recently J. Bokowski significantly
contributed to this topic; see their papers in this volume. We celebrate
the double-jubilee by the first ever Császár-Crowe-Szilassi-Bokowski
meeting and by reprinting Császár’s paper of 1949.
Note that this is not in the main stream of Császar’s works
in general topology, but still his favorite among the “other”
contributions (cf., the interview and papers in the “Supplement”
to the journal Természet Világa, November 1994, in Hungarian,
which celebrated the 70th birthday of Császár). [D. Nagy] |