I've encountered the following quartic quadrivariate polynomial, \begin{equation} \left(w^2-1\right) x^2-w^2-2 w x y z+\left(y^2-1\right) \left(z^2-1\right). \end{equation} Does it correspond to any recognizable, previously-studied surface (if equated to 0)?
This polynomial appears in a certain quantum-information-theoretic context, pertaining to the probability (with respect to Hilbert-Schmidt measure) that a two-qubit system is separable/disentangled.