Geodesic
Triangular and quadrangular pyramids in a three-dimensional normed space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 42-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main results are as follows. Every three-dimensional real normed space contains an isometrically embedded set of vertices of a Euclidean tetrahedron whenever the ratio of lengths for each pair of edges of the tetrahedron is $\ge(\sqrt{8/3}+1)/3<0.878$. Every three-dimensional normed space contains an affine image of a regular quadrangular pyramid having lateral edges of equal length, base edges of equal length, and base diagonals of equal length, having a predetermined ratio $>\sqrt{2/3}$ of the length of the lateral edge to the length of the base edge. 
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V. V. Makeev. Triangular and quadrangular pyramids in a three-dimensional normed space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 12, Tome 415 (2013), pp. 42-50. http://geodesic.mathdoc.fr/item/ZNSL_2013_415_a6/

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