 The great grand stellated 120-cell is the "final stellation" of the 120-cell, and is the only Schläfli-Hess polychoron to have the 120-cell for its convex hull.In this sense it is analogous to the three-dimensional great stellated dodecahedron, which is the final stellation of the dodecahedron and the only Kepler-Poinsot polyhedron to have the dodecahedron for its convex hull.Indeed, the great grand stellated 120-cell is dual to the grand 600-cell, which could be taken as a 4D analogue of the great icosahedron, dual of the great stellated dodecahedron.