  We study an extreme scenario of the Mastrand projection theorem for which a
fractal has the property that its orthogonal projection is the same as the
orthogonal projection of its convex hull. We extend results in current
literature and establish checkable criteria for self-affine sets to have such
property. Using this, we show that every convex polytope on $\R^d$ contains a
totally disconnected compact set, which is a union of self-affine sets, of
dimension as close to 1 as possible, as well as a rectifiable 1-set, such that
the fractal projects to an interval in every 1-dimensional subspace and its
convex hull is the given polytope. Other convex sets and projections onto
higher dimensional subspaces will also be discussed.
