Document Type
Article - preprint
Department
Mathematics (HMC)
Publication Date
4-2005
Abstract
We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their exterior faces.
Rights Information
© 2005 Springer-Verlag
Terms of Use & License Information
DOI
10.1007/s00454-004-1128-0
Recommended Citation
Adam Bliss and Francis Edward Su. Lower bounds for simplicial covers and triangulations of cubes. Discrete Comput. Geom., 33(4):669–686, 2005.
Included in
Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons, Numerical Analysis and Computation Commons
Comments
Author's pre-print manuscript available for download.
For the publisher's version, please visit http://dx.doi.org/10.1007/s00454-004-1128-0.