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From binary cube triangulations to acute binary simplices. (English) Zbl 1313.65032

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 31-42 (2012).
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 the authors 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. The authors continue with the study of such acute binary simplices and point out their possible relation to the Hadamard determinant problem.
For the entire collection see [Zbl 1277.00031].

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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