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From binary cube triangulations to acute binary simplices

Brandts, Jan; van den Hooff, Jelle; Kuiper, Carlo; Steenkamp, Rik — 2012

Applications of Mathematics 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 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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