Twisted sums, Fenchel-Orlicz spaces and property (M)

We study certain twisted sums of Orlicz spaces with non-trivial type which can be viewed as Fenchel-Orlicz spaces on ${\rm {\bf R}}^2$. We then show that a large class of Fenchel-Orlicz spaces on ${\rm {\bf R}}^n$ can be renormed to have property (M). In particular this gives a new construction of the twisted Hilbert space $Z_2$ and shows it has property (M), after an appropriate renorming.