On 0/1-polytopes with nonobtuse triangulations

Recently, Brandts et al. (2013) [5] studied 0/1-triangulations of the unit n-cube In with simplices that only have nonobtuse dihedral angles. An example is the standard triangulation into n! simplices. It is proved in [5] that for each n ≥ 3 there is essentially only one other nonobtuse 0/1-triangulation of In. Here we will outline an investigation into 0/1-triangulations of other 0/1-polytopes with simplices that only have nonobtuse dihedral angles. As far as we know, this is the only source that combines both concepts 0/1-polytopes and nonobtuse 0/1-triangulations. In particular, we investigate nonobtuse 0/1-triangulations of 0/1-polytopes in I3 and I4.