Grand 600-cell

In geometry, the grand 600-cell or grand polytetrahedron is a regular star 4-polytope with Schläfli symbol {3,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is the only one with 600 cells.

It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.

It has the same edge arrangement as the great stellated 120-cell, and grand stellated 120-cell, and same face arrangement as the great icosahedral 120-cell. As the only stellation of the 600-cell among the Schläfli-Hess polytopes, it could be taken as analogous to the three-dimensional great icosahedron, the only stellation of the icosahedron among the Kepler-Poinsot polyhedra. Indeed, the great 600-cell is dual to the great grand stellated 120-cell, which could be taken as a 4D analogue of the great stellated dodecahedron, dual of the great icosahedron.

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