Geodesic
On unique recoverability of convex and visible compacta from their projections
Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 1-10

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The question is: Under what conditions does the congruence of the projections of two compacta on every two-dimensional plane imply the congruence of the compacta themselves? The results are extended to the cases of $(n-2)$-visible and $(n-2)$-convex compacta, and even to the case when it is known the projections of the compacta are merely similar. 
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     author = {V. P. Golubyatnikov},
     title = {On unique recoverability of convex and visible compacta from their projections},
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V. P. Golubyatnikov. On unique recoverability of convex and visible compacta from their projections. Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/SM_1992_73_1_a0/