Isosceles tetrahedrons with integer edges and volume in the grid
Robert Brawer
Solothurn, Switzerland
![Isosceles tetrahedrons with integer edges and volume in the $\mathbb{Z}\times\mathbb{Z}\times\mathbb{Z}$ grid cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-em-volume-78-issue-3.png&w=3840&q=90)
Abstract
By adding parallelogram identities, we prove an equation on the edge lengths of a tetrahedron and the diagonal lengths of its medial octahedron. By this and with the help of Euler bricks we find in the grid a family of isosceles tetrahedrons with integer edge length and integer volume.
Cite this article
Robert Brawer, Isosceles tetrahedrons with integer edges and volume in the grid. Elem. Math. 78 (2023), no. 3, pp. 123–126
DOI 10.4171/EM/475