  For any $n$-dimensional simplex in the Euclidean space $\mathbb{R}^n$ with
$n\ge 4$, it is asked that if a continuous deformation preserves the volumes of
all the codimension 2 faces, then is it necessarily a \emph{rigid} motion.
While the question remains open and the general belief is that the answer is
affirmative, for all $n\ge 4$, we provide counterexamples to a variant of the
question where $\mathbb{R}^n$ is replaced by a pseudo-Euclidean space
$\mathbb{R}^{p,n-p}$ for some unspecified $p\ge 2$.
