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

Projections of totally disconnected thin fractals with very thick shadows on ${\mathbb R}^d$