Instanton numbers and exchange symmetries in N = 2 dual string pairs

In this note, we comment on Calabi-Yau spaces with Hodge numbers h1,1 = 3 and h2,1 = 243. We focus on the Calabi-Yau space WP1,1,2,8,12 (24) and show how some of its instanton numbers are related to coefficients of certain modular forms. We also comment on the relation of four-dimensional exchange symmetries in certain N = 2 dual models to six-dimensional heterotic/heterotic string duality.