Problem #170

A regular tetrahedron with sides of length 1 (blue in the figure below) is surrounded by four other regular tetrahedra with sides of length 1 so that each of the four surrounding tetrahedra shares a face with the central tetrahedron. The four unshared vertices (one from each of the surrounding tetrahedra) form the vertices of a larger tetrahedron (red in the figure below). What is the length of one side of the larger tetrahedron?

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