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Article

Brandts, Jan ; van den Hooff, Jelle ; Kuiper, Carlo ; Steenkamp, Rik
From binary cube triangulations to acute binary simplices. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 31-42
MSC: 65D18 | MR 3204398 | Zbl 1313.65032
Keywords:
$0/1$-simplex; acute simplex; Hadamar determinant problem; binary cube triangulations
Summary:
Cottle's proof that the minimal number of $0/1$-simplices needed to triangulate the unit $4$-cube equals $16$ uses a modest amount of computer generated results. In this paper we remove the need for computer aid, using some lemmas that may be useful also in a broader context. One of the $0/1$-simplices involved, the so-called antipodal simplex, has acute dihedral angles. We continue with the study of such acute binary simplices and point out their possible relation to the Hadamard determinant problem.
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