The 10 edge lengths of a 4-simplex with vertices $0,1,2,3,4$ satisfy the inequality that the eigenvalues of the matrix $M$ with elements $$M = [m_{ij}] = l_{0i}^2+l_{0j}^2-l_{ij}^2$$ is positive definite. $l_{ij}$ is the length of an edge connecting vertices $i$ and $j$. This actually holds in general for an $n$-simplex. A 4-simplex also has 10 areas of triangles.
My question is that given rather 10 areas of triangles of the 4-simplex, is there an inequality between only the areas to ensure that they form the simplex?