On pyramids in a three-dimensional normed space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 132-138 Cet article a éte moissonné depuis la source Math-Net.Ru

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For Euclidean tetrahedra of special type it is proved that their vertex set can be isometrically embedded in an arbitrary three-dimensional normed space. In particular, this is true for every regular triangular pyramid. Bibl. – 10 titles.
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V. V. Makeev. On pyramids in a three-dimensional normed space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 132-138. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a11/

[1] P. Brass, “On equilateral simplices in normed spaces”, Beiträge Algebra Geom., 40 (1999), 303–307 | MR | Zbl

[2] A. Dvoretzky, “Some results on convex bodies and Banach spaces”, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960), Pergamon, Oxford, 1961, 123–160 | MR

[3] B. Grünbaum, “Affineregular polygons inscribed in plane convex sets”, Riveon Lematematika, 13 (1959), 20–24 | MR

[4] S. A. Kakutani, “A proof that there exists a circumscribing cube around any bounded closed set in $\mathbb R^3$”, Ann. of Math., 43 (1942), 739–741 | DOI | MR | Zbl

[5] C. Petty, “Equilateral sets in Minkowski spaces”, Proc. Amer. Math. Soc., 27 (1971), 369–374 | DOI | MR

[6] V. V. Makeev, “O ravnobedrennykh simpleksakh v chetyrekhmernom normirovannom prostranstve”, Zap. nauch. semin. POMI, 329, 2005, 88–91 | MR | Zbl

[7] V. V. Makeev, “Prostranstvennye obobscheniya nekotorykh teorem o vypuklykh figurakh”, Mat. zametki., 36 (1984), 405–415 | MR | Zbl

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

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

[10] L. G. Shnirelman, “O nekotorykh geometricheskikh svoistvakh zamknutykh krivykh”, Uspekhi mat. nauk, 1944, no. 10, 34–44 | MR | Zbl