  We consider Jacobi matrices with zero diagonal and off-diagonals given by
elements of the hull of the Fibonacci sequence and show that the spectrum has
zero Lebesgue measure and all spectral measures are purely singular continuous.
In addition, if the two hopping parameters are distinct but sufficiently close
to each other, we show that the spectrum is a dynamically defined Cantor set,
which has a variety of consequences for its local and global fractal dimension.
