Abstract
Let K and L be two convex bodies in R4, such that their projections onto all 3-dimensional subspaces are directly congruent. We prove that if the set of diameters of the bodies satisfies an additional condition and some projections do not have certain π-symmetries, then K and L coincide up to translation and an orthogonal transformation. We also show that an analogous statement holds for sections of star bodies, and prove the n-dimensional versions of these results.
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Supported in part by U.S. National Science Foundation Grant DMS-1100657.
Supported in part by U.S. National Science Foundation Grants DMS-0652684 and DMS-1101636.
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Alfonseca, M.A., Cordier, M. & Ryabogin, D. On bodies with directly congruent projections and sections. Isr. J. Math. 215, 765–799 (2016). https://doi.org/10.1007/s11856-016-1394-6
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DOI: https://doi.org/10.1007/s11856-016-1394-6