12. Reducing the volume of a single simplex (30.06.15).

Aim of the talk: Show that with one dilation-refinement step one can reduce the maximal volume for a single simplex.

Details: Box points in dilates; prove [HPPS14, Lemma 4.13] and also [HPPS14, Lemma 4.14] for the case $k=d$ of a full-dimensional carrier, omit regularity (coordinate with talk #13).

N.N.