Lajos Szilassi (born 1942 in Szentes, Hungary) was a professor of mathematics at the University of Szeged who worked in projective and non-Euclidean geometry, applying his research to computer generated solutions of geometric problems. [1]
Lajos Szilassi (born 1942 in Szentes, Hungary) was a professor of mathematics at the University of Szeged who worked in projective and non-Euclidean geometry, applying his research to computer generated solutions of geometric problems. [1]
Szilassi obtained his high school diploma in 1966 at the Bolyai Institute of the József Attila University, majoring in mathematical representation geometry. He had been teaching for six years in a secondary school, then he joined the Department of Mathematics at Gyula Juhász Teacher Training College. [2] In 1981 he received a bachelor's associate degree. He then received his Doctor rerum naturalium degree at the University of Szeged (1978) under László Lovász with the dissertation Polyhedra bounded by pairwise adjacent faces. [3] He received his PhD in 2006. [4]
From 1973 until he retired in 2007 he was a professor of mathematics at the University of Szeged. [5] He worked in the areas of geometry, elementary mathematics, and computer science, with an emphasis on computer generated solutions of geometric problems.
In 1977 Szilassi discovered a toroidal polyhedron with seven hexagonal faces, in which each pair of faces share an edge. The new construction was soon dubbed the Szilassi polyhedron. [6] This is mathematically significant because the tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face. Martin Gardner featured the Szilassi polyhedron in his November 1978 Mathematical Games column in Scientific American . [7]
On April 29, 2002 the French government installed a sculpture of the "Szilassi-Polyhedron" in the town of Beaumont-de-Lomagne, the birthplace of Fermat, on the 400th anniversary of his birth. [8] There are also large scale renderings of the polyhedron in Canberra, Australia [9] and in Whitehall, Michigan. [10]
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids, excluding the prisms and antiprisms, and excluding the pseudorhombicuboctahedron. They are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices.
In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k – 1)-polytopes in common.
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces, 36 edges, and 24 vertices.
In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges. Since each of its faces has point symmetry, the truncated cuboctahedron is a 9-zonohedron. The truncated cuboctahedron can tessellate with the octagonal prism.
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron or omnitruncated icosahedron is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.
The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular prism by attaching equilateral square pyramids to each of its three square faces. The same shape is also called the tetrakis triangular prism, tricapped trigonal prism, tetracaidecadeltahedron, or tetrakaidecadeltahedron; these last names mean a polyhedron with 14 triangular faces. It is an example of a deltahedron and of a Johnson solid.
In geometry, the Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces.
Father Magnus J. Wenninger OSB was an American mathematician who worked on constructing polyhedron models, and wrote the first book on their construction.
A noble polyhedron is one which is isohedral and isogonal. They were first studied in any depth by Hess and Bruckner in the late 19th century, and later by Grünbaum.
A heptahedron is a polyhedron having seven sides, or faces.
In geometry, the Császár polyhedron is a nonconvex toroidal polyhedron with 14 triangular faces.
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs.
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid, having a topological genus of 1 or greater. Notable examples include the Császár and Szilassi polyhedra.
Bolyai Institute is the mathematics institute of the Faculty of Sciences of the University of Szeged, named after the Hungarian mathematicians, Farkas Bolyai, and his son János Bolyai, the co-discoverer of non-Euclidean geometry. Its director is László Zádori. Among the former members of the institute are Frigyes Riesz, Alfréd Haar, Rudolf Ortvay, Tibor Radó, Béla Szőkefalvi-Nagy, László Kalmár, Géza Fodor.
Andor Kertész was a Hungarian mathematician and professor of Mathematics at the Lajos Kossuth University (KLTE), Debrecen. He is the father of linguist András Kertész.
Árpád Varecza, was a Hungarian mathematician, former lecturer at the College of Nyíregyháza, head of the Institute of Mathematics and Informatics, and deputy director general of the institution for three years.
Adventures Among the Toroids: A study of orientable polyhedra with regular faces is a book on toroidal polyhedra that have regular polygons as their faces. It was written, hand-lettered, and illustrated by mathematician Bonnie Stewart, and self-published under the imprint "Number One Tall Search Book" in 1970. Stewart put out a second edition, again hand-lettered and self-published, in 1980. Although out of print, the Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries.