A new proof shows that every origin-symmetric convex body K in R^3 satisfies |K| |K^o| >= 32/3 via symmetric admissible shadow systems.
Saint-Raymond,Sur le volume des corps convexes symétriques, Séminaire d’Initiation à l’Analyse, 1980–1981, Exp
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The Symmetric Mahler Inequality in Dimension Three via Admissible Shadow Systems
A new proof shows that every origin-symmetric convex body K in R^3 satisfies |K| |K^o| >= 32/3 via symmetric admissible shadow systems.