Minimal Simplicial Dissections and Triangulations of Convex 3-Polytopes |
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| Authors: | A Below U Brehm J A De Loera and J Richter-Gebert |
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| Institution: | (1) Institut für Theoretische Informatik, ETH-Zürich, CH-8092 Zürich, Switzerland below.richter@inf.ethz.ch, CH;(2) Institut für Geometrie, Technische Universität Dresden, 01062 Dresden, Germany brehm@math.tu-dresden.de , DE;(3) Department of Mathematics, University of California at Davis, Davis, CA 95616-8633, USA deloera@math.ucdavis.edu, US |
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| Abstract: | This paper addresses three questions related to minimal triangulations of a three-dimensional convex polytope P .
• Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices?
• Can a dissection of P use fewer tetrahedra than a triangulation?
• Does the size of a minimal triangulation depend on the geometric realization of P ?
The main result of this paper is that all these questions have an affirmative answer. Even stronger, the gaps of size produced
by allowing interior vertices or by using dissections may be linear in the number of points.
Received August 16, 1999, and in revised form February 29, 2000. Online publication May 19, 2000. |
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