Two distinct regular tetrahedra have all their vertices among the vertices of the same unit cube. What is the volume of the region formed by the intersection of the tetrahedra?

**Answer Choices**

A. \dfrac{1}{12}

B. \dfrac{\sqrt{2}}{12}

C. \dfrac{\sqrt{3}}{12}

D. \dfrac{1}{6}

E. \dfrac{\sqrt{2}}{6}