Pyramids in three-dimensional normed spaces (Q844474)

The paper deals with isometrical embeddings of pyramids into 3-dimensional normed spaces. It was proved by \textit{C. M.~Petty} [Proc. Am. Math. Soc. 29, 369--374 (1971; Zbl 0214.20801)] that every 3-dimensional normed space contains 4 points lying at equal distances from each other. In the present paper the author proves that the vertex set of a tetrahedron can be isometrically embedded into any 3-dimensional normed space under certain conditions on the vertex set. Some results on isometrical embeddings of quadrangular pyramids are also provided.