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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 ofall 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 isaffirmative, for all $n\ge 4$, we provide counterexamples to a variant of thequestion where $\mathbb{R}^n$ is replaced by a pseudo-Euclidean space$\mathbb{R}^{p,n-p}$ for some unspecified $p\ge 2$.

Simplices with fixed volumes of codimension 2 faces in a continuous deformation