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Theorem 4.1 of this paper by Klee says yes. Moreover, the result generalizes to higher dimensions and higher-codimensional for projections (as long as you look at at least 2-dimensional projections)of arbitrary dimension $\ge 2$.

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Theorem 4.1 of this paper says yes. Moreover, the result generalizes to higher dimensions and higher-codimensional projections (as long as you look at at least 2-dimensional projections).