Projection areas of convex bodies in R^4 and homology classes of surfaces in (P^1)^4 are both characterized by the same Lorentzian matrix condition, which is the Plücker condition over the triangular hyperfield.
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Realizations of homology classes and projection areas
Projection areas of convex bodies in R^4 and homology classes of surfaces in (P^1)^4 are both characterized by the same Lorentzian matrix condition, which is the Plücker condition over the triangular hyperfield.