  We solve a very classical problem motivated by considerations in quantum
gravity: providing a description of the geometry of a Euclidean tetrahedron
from the initial data of the areas of the faces and the areas of the medial
parallelograms of Yetter or equivalently of the pseudofaces of McConnell. In
particular, we derive expressions for the dihedral angles, face angles and (an)
edge length, the remaining parts being derivable by symmetry or by identities
in the classic 1902 compendium of results on tetrahedral geometry of
Richardson.
  We also provide an alternative proof using (bi)vectors of the result of
Yetter that four times the sum of the squared areas of the medial
parallelograms is equal to the sum of the squared areas of the faces.
  The updated version corrects several errors and provides better historical
context for the result.
