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Three-dimensional del Pezzo varieties of degree 2 are double covers ofprojective space $\mathbb{P}^{3}$ branced in a quadric. In this paper we provethat if a del Pezzo variety of degree 2 has exactly 15 nodes then thecorresponding quadric is a hyperplane section of the Igusa quartic or,equivalently, all such del Pezzo varieties are members of one particular linearsystem on the Coble fourfold. Their automorphism groups are induced from theautomorphism group of Coble fourfold. Also we classify all $G$-birationallyrigid varieties of such type.

Biregular and birational geometry of quartic double solids with 15 nodes