TY - GEN A1 - Ziegler, Günter M. T1 - Lectures on Polytopes. N2 - These lecture notes have several aims: \begin{itemize} \item to give an introduction to some basic facts about convex polytopes, with an emphasis on the basic methods that yield them (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms and oriented matroids), \item to discuss some important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associahedra, fiber polytopes, the Lawrence construction) \item and to illustrate why polytope theory is exciting, with highlights like Kalai's new diameter bounds, the construction of non-rational polytopes, the Bohne-Dress tiling theorem, shellability and the upper bound theorem, .... \end{itemize} For several of these topics the decisive break-through is very recent, which suggests that there is much more discovered. T3 - ZIB-Report - TR-93-06 Y1 - 1993 N1 - No preprint available; published as Ziegler, G. M. (1994) Lectures on Polytopes. ISBN 354094365X, New York: Springer ER - TY - JOUR A1 - Ziegler, Günter M. A1 - Hege, Hans-Christian A1 - Duda, Georg T1 - Neue Bilder für die Medizin? JF - DFN-Mitteilungen Y1 - 2005 VL - 13(3) SP - 163 EP - 167 ER - TY - CHAP A1 - Polthier, Konrad A1 - Bobenko, Alexander A1 - Hildebrandt, Klaus A1 - Kornhuber, Ralf A1 - Tycowicz, Christoph von A1 - Yserentant, Harry A1 - Ziegler, Günter M. T1 - Geometry processing T2 - MATHEON - Mathematics for Key Technologies Y1 - 2014 SN - 978-3-03719-137-8 U6 - https://doi.org/10.4171/137 VL - 1 SP - 341 EP - 355 PB - EMS Publishing House ER - TY - GEN A1 - Polthier, Konrad A1 - Sullivan, John A1 - Ziegler, Günter M. A1 - Hege, Hans-Christian ED - Deuflhard, Peter ED - et al., T1 - Visualization T2 - MATHEON - Mathematics for Key Technologies Y1 - 2014 SN - 978-3-03719-137-8 U6 - https://doi.org/10.4171/137 SP - 335 EP - 339 PB - European Mathematical Society ER - TY - JOUR A1 - Sanyal, Raman A1 - Werner, Axel A1 - Ziegler, Günter T1 - On Kalai’s conjectures concerning centrally symmetric polytopes. JF - Discrete Comput. Geom. Y1 - 2009 U6 - https://doi.org/10.1007/s00454-008-9104-8 VL - 41 IS - 2 SP - 183 EP - 198 ER -