From binary cube triangulations to acute binary simplices

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