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.

EUDML-ID : urn:eudml:doc:287847
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Mots clés:

@article{702890,
     title = {From binary cube triangulations to acute binary simplices},
     booktitle = {Applications of Mathematics 2012},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2012},
     pages = {31-42},
     mrnumber = {MR3204398},
     zbl = {1313.65032},
     url = {http://dml.mathdoc.fr/item/702890}
}

Brandts, Jan; van den Hooff, Jelle; Kuiper, Carlo; Steenkamp, Rik. From binary cube triangulations to acute binary simplices, dans Applications of Mathematics 2012, GDML_Books,  (2012), pp. 31-42. http://gdmltest.u-ga.fr/item/702890/