On the Number of Congruent Classes of the Tetrahedra Determined by Given Volume, Circumradius and Face Areas

Zhenbing Zeng, Lu Yang, Lydia Dehbi

Abstract: In this paper, we proved that for any tetrahedron T, there exists at least one, at most eight non-congruent tetrahedra so that they share the same volume, circumradius and four face areas. We used metric invariants of tetrahedra to construct the equation system and investigated the number of its real rootswith symbolic computation. We also posed one open problem on the basis of extensive numerical computation.