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I'd like to plot in tikz the below constraint on the unit cube defined by the region x, y, z in [-1, 1].

x^2 + y^2 + z^2 - 2 * x * y * z <= 1

I found Making a 3D colored pyramid in tikz though it doesn't work with the above constraint.

The following is the graph from http://www.jstor.org/stable/10.2307/2684832. I'd prefer it to look more "modern" or similar to the 3d pyramid style.

Any help is much appreciated.

enter image description here

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