The Brown-Comenetz dual of the K(2)-local sphere at the prime 3

We calculate the homotopy type of the Brown-Comenetz dual I2 of the K(2)-local sphere at the prime 3 and show that there is an equivalence in the K(2)-local category between I2 and a smash product of the determinant twisted sphere and an exotic element P in the Picard group. We give a characterization of P as well. A secondary aim of the paper is to extend our library of calculations in the K(2)-local category.