WiSe 16/17: Seminar zur Diskreten Geometrie
This seminar will look at tilings.
We start with planar tilings, their properties, their generation e.g. by crystallographic groups, as well as at attempts of classification. (This quickly leads us to unsolved problems. For example, which pentagons tile the plane by congruent copies?)
Then we look at 3-dimensional tilings and their properties. New questions arise here: Which (combinatorial types of) polyhedra can be used to tile space? How many faces can a polyhedron have whose congruent copies tile space?
-- this seminar will mostly take place in English --
Federico Ardila und Richard P. Stanley: Pflasterungen, Math. Semesterberichte 53 (2006), 17-43.
John H. Conway and Jeffrey C. Lagarias: Tiling with polyominoes and combinatorial group theory, J. Combinat. Theory, Ser. A, 53 (1990), 183-208.
David Eppstein, John M. Sullivan and Alper Ungor: Tiling space and slabs with acute tetrahedra, Comput. Geometry: Theory & Applications 27 (2004), 237-255.
Branko Grünbaum and Geoffrey C. Shephard: Tilings with congruent tiles, Bull. Amer. Math. Soc. 3 (1980), 951-973.
Branko Grünbaum and Geoffrey C. Shephard: Tilings and Patterns, Freeman 1987.
Egon Schulte: Tilings, in: Handbook of Convex Geometry (P. Gruber and J. Wills, eds.), North-Holland, Amsterdam 1993, 899-932.
16 Class schedule
Inhalt:This seminar will look at tilings. We start with planar tilings, their properties, their generation e.g. by crystallographic groups, as well as at attempts of classification. ... read more