While theoretically possible, it&#x27;ll be very difficult to realize physically.  If you allow fractal constructions, purely unrectifiable sets can fit the bill.  For example, here&#x27;s an example in 2-dimensional space that casts a solid shadow when the light source is along one axis but not from any other: <a href="https:&#x2F;&#x2F;books.google.com&#x2F;books?id=usjNBQAAQBAJ&amp;lpg=PP1&amp;dq=&amp;pg=PA34#v=onepage&amp;q&amp;f=false" rel="nofollow">https:&#x2F;&#x2F;books.google.com&#x2F;books?id=usjNBQAAQBAJ&amp;lpg=PP1&amp;dq=&amp;p...</a>