Student Co-author

HMC Undergraduate

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.

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.

Rights Information

© 2005 Springer-Verlag

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