$0/1$-simplex; acute simplex; Hadamar determinant problem; binary cube triangulations
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.