Geodesic
Description of a class of solids in~$\mathbb R^3$
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 149-164

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Let $Q\subset\mathbb R^3$ be a compact convex solid such that for each parallel (not necessarily orthogonal) projection onto any plane no two antipodal faces of the solid are projected strictly inside the projection of all $Q$. Then $Q$ is either a cone with a convex base or a frustrum of a trihedral pyramid or a prism (possibly with nonparallel bases). 
@article{ZNSL_1998_252_a13,
     author = {N. D. Lebedeva},
     title = {Description of a class of solids in~$\mathbb R^3$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--164},
     publisher = {mathdoc},
     volume = {252},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a13/}
}
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N. D. Lebedeva. Description of a class of solids in~$\mathbb R^3$. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 149-164. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a13/