Tetraeder with equal sides (Q670712)

The paper under review investigates properties of thetrahedra such that all its 6 sides are equal. For example, it is proved (Theorem 2) that a tetrahedron has all 6 sides equal if and only if it has equal opposite sides (understanding opposite in the obvious way). We also find results as Theorem 6 stating that a tetrahedron has all 6 sides equal if and only if its center of gravity coincides with the center of its circumbscribed sphere. The paper (in German) is of elementary nature and easy to read. It would make an interesting undergraduate assignment.