I really want to say the volume of a tetrahedron is something like a constant (maybe 1/6) times the determinant of the 4x4 matrix of points. This would be relat

I really want to say the volume of a tetrahedron is something like a constant (maybe 1/6) times the determinant of the 4x4 matrix of points. This would be related to what you said. Take the determinant by expansion along the row of 1's, which results in the sum of 4 sub-determinants which... I don't remember ;-)