There are lots of dualities: the wave/particle duality; in the Hilbert space, there is a duality between the bra and the ket vectors, and so on. The word "duality" simply means "two". Wherever there are two kinds of things that are somewhat related, there is a duality. In String Theory, the dualities are related to some transformations: in one case, called T-duality, the two string theories are related by the transformation of the distances: R → 1/R. The types IIa with IIB, and Heterotic E8xE8 with Heterotic SO(32) are T-duals. While the S-duality is related by the couplig transformation, g→ 1/g. The types I with Heterotic SO(32), and type IIB with itself are S-duals.
Well, yes, I understand that part, but I noticed a possibly interesting link, specifically between the Platonic solids and the dualities of the coupling constants in string theory.
I was reading a book about symmetry (appropriately titled "Symmetry") by Marcus du Sautoy, in which he discusses these Platonic dualities (pg. 57-58). The cube is dual to the octahedron, the dodecahedron is dual to the icosahedron, and the tetrahedron is dual to itself. This reminded me of reading about the coupling strength dualities of the various string theories in Brian Greene's book "The Elegant Universe" (pg. 313) in which he says that the coupling strength of Type-I is dual to the coupling strength of Heterotic-SO(32), the coupling strength of Heterotic-E8xE8 is dual to the coupling strength of type-IIA, with type IIB being dual to itself.
It just seemed to me to be of a similar pattern, and I thought there could be some subtle connection. But I'm neither scientist nor mathematician enough to be able to tell if there is any significance to this.