Smallest amount of planes to enclose a closed space in extended projective geometry $\mathbb R^3_{\pm\infty}$

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The smallest amount of planes to enclose a polyhedron is 4 in the euclidean $\mathbb R^3$ where it encloses a tetrahedron. What is the smallest amount of planes to enclose a closed space in extended euclidean geometry aka projective geometry where you suppose infinities as points?