Does a certain quartic quadrivariate polynomial fall within any known category?

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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)?