Fig. 5: An alternative (D2) arrangement of the five Platonic solids.
From: A Keplerian Ag90 nest of Platonic and Archimedean polyhedra in different symmetry groups

a Views of the quintuple nest, arbitrarily scaled, slightly off a twofold axis, b along four- and twofold axes, c along twofold axes (with edges at right angles), and d along twofold axes (with edges parallel). e Views of the double 555 and 444 nest along two- and fourfold axes, f along twofold axes (with edges at right angles, corresponding to c), and g along twofold axes (with edges parallel, corresponding to d). h Views of the double 444 and 333 nest along four- and twofold axes and i along twofold axes. With just three (orthogonal) twofold axes, each one different from the other, but with no mirrors, this regular quintuple nest has D2 symmetry.