Geodesic
On PL embeddings of a 2-sphere in the 4-dimensional Euclidean space
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 867-883 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that there is no 2-convex $ PL $ embedding of $S^2$ in $ E^4$ in the form of a polyhedron, each vertex of which is incident to no more than 5 edges.
Keywords: polyhedron, PL embedding, Euclidean space. 
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     author = {D. V. Bolotov},
     title = {On {PL} embeddings of a 2-sphere in the 4-dimensional {Euclidean} space},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {867--883},
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D. V. Bolotov. On PL embeddings of a 2-sphere in the 4-dimensional Euclidean space. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 867-883. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a28/

[1] Yu.B. Zelinskii, Convexity. Selected chapters, Instytut Matematyky NAN Ukrainy, Kyiv, 2012 | Zbl

[2] D.V. Bolotov, “On embeddings of $S^2$ in $E^4$”, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 11 (2013), 19–22 (Russian) | MR | Zbl