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Omni-MATH / ABCD is a regular tetrahedron of volume 1. Maria glues regular tetrahedra A^{prime} B C D, A B^{prime} C D, A B C^{prime} D, and A B C D^{prime} to the faces of ABCD. What is the v…

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problem

ABCDA B C D is a regular tetrahedron of volume 1. Maria glues regular tetrahedra $A^{\prime} B C D, A B^{\prime} C D$, $A B C^{\prime} D$, and $A B C D^{\prime}$ to the faces of ABCDA B C D. What is the volume of the tetrahedron $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$?
Plain-text mathematical notation (without MathML)
ABCD is a regular tetrahedron of volume 1. Maria glues regular tetrahedra $A^{\prime} B C D, A B^{\prime} C D$, $A B C^{\prime} D$, and $A B C D^{\prime}$ to the faces of ABCD. What is the volume of the tetrahedron $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$?
Original LaTeX notation
$A B C D$ is a regular tetrahedron of volume 1. Maria glues regular tetrahedra $A^{\prime} B C D, A B^{\prime} C D$, $A B C^{\prime} D$, and $A B C D^{\prime}$ to the faces of $A B C D$. What is the volume of the tetrahedron $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$?

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