The most well known case of Routh's triangle theorem is: 

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> If the sides BC, CA,and AB are trisected at the points D, E, and F, respectively, then the area of the inside triangle formed by AD, BE, CF is $\dfrac{1}{7}$th of the area of that of the triangle ABC.
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**Here is my question:** can Routh's theorem be generalized to a tetrahedron which is cut by 4 planes through its 4 vertices and cutting the opposite faces appropriately?

As far as I know, this question has never been contemplated in the literature.