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