Geodesic
Polygons inscribed in a closed curve and a three-dimensional convex body
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 116-125 
V. V. Makeev. Polygons inscribed in a closed curve and a three-dimensional convex body. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 116-125. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a9/
@article{ZNSL_2008_353_a9,
     author = {V. V. Makeev},
     title = {Polygons inscribed in a~closed curve and a~three-dimensional convex body},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--125},
     year = {2008},
     volume = {353},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Here are samples of results obtained in the paper. Let $\gamma$ be a centrally symmetric closed curve in $\mathbb R^n$ that does not contain its center of symmetry, $O$. Then $\gamma$ is circumscribed about a square (with center $O$), and about a rhombus (also with center $O$) whose vertices split $\gamma$ into parts of equal length. If $n$ is odd, then there is a centrally symmetric equilateral $2n$-link polyline inscribed in $\gamma$ and lying in a hyperplane. Let $K\subset\mathbb R^3$ be a convex body, $x\in(0;1)$. Then $K$ is circumscribed about an affine-regular pentagonal prism $P$ such that the ratio of the lateral edge $l$ of $P$ to the longest chord of $K$ parallel to $l$ is equal to $x$. Bibl. – 7 titles.

[1] V. V. Makeev, “Zadacha Knastera i pochti sfericheskie secheniya”, Mat. sb., 180:3 (1989), 424–431 | MR | Zbl

[2] V. V. Makeev, “O pyatiugolnikakh, vpisannykh v zamknutuyu krivuyu i ee vershinakh”, Zap. nauchn. semin. POMI, 246, 1997, 184–190 | MR | Zbl

[3] V. V. Makeev, “O dvukh nereshennykh geometricheskikh zadachakh”, Zap. nauchn. semin. POMI, 280, 2001, 211–218 | MR | Zbl

[4] V. V. Makeev, “Trekhmernye mnogogranniki, vpisannye i opisannye vokrug vypuklykh kompaktov. II”, Algebra i analiz, 13:5 (2001), 110–133 | MR | Zbl

[5] V. V. Makeev, “O nekotorykh geometricheskikh svoistvakh vypuklykh tel. II”, Algebra i analiz, 15:6 (2003), 74–85 | MR | Zbl

[6] V. V. Makeev, “O nekotorykh geometricheskikh svoistvakh zamknutykh prostranstvennykh krivykh i vypuklykh tel”, Algebra i analiz, 16:5 (2004), 92–100 | MR

[7] V. V. Makeev, “O chetyrekhugolnikakh, vpisannykh v zamknutuyu krivuyu, i ee vershinakh”, Zap. nauch. semin. POMI, 299, 2003, 241–251 | MR