MathNet 2009-part-05 — 172 problems (EN–VI) Question 63

$ABCD$ is a regular tetrahedron of volume $1$. Maria glues regular tetrahedra $A'BCD$, $AB'CD$, $ABC'D$, and $ABCD'$ to the faces of $ABCD$. What is the volume of the tetrahedron $A'B'C'D'$?