Error in linear interpolation at the vertices of a simplex

• Pavel Shvartsman's sharp pointwise error bound was published in at-net in '94.
• There is a rather detailed paper by Shayne Waldron from 1994, on `The error in linear interpolation at vertices of a simplex' that appeared in \SJNA; 35(3); 1998; 1191--1200;
• Some simple geometric facts about balls and simplices.