We give a simple example that disproves the following 2015 conjecture of Lacoste-Julien and Jaggi concerning the pyramidal width (aka facial distance):
The pyramidal width of a set of vertices is non-increasing when another vertex is added (assuming that all previous points remain vertices).
In contrast to the recent example by Zhao (arXiv:2607.29555), our counterexample is readily verifiable via visual inspection. Furthermore, our counterexample shows that the relative increase in the pyramidal width can be arbitrarily large.