Great grand stellated 120-cell | |
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Orthogonal projection | |
Type | Schläfli-Hess polychoron |
Cells | 120 {5/2,3} |
Faces | 720 {5/2} |
Edges | 1200 |
Vertices | 600 |
Vertex figure | {3,3} |
Schläfli symbol | {5/2,3,3} |
Coxeter-Dynkin diagram | |
Symmetry group | H4, [3,3,5] |
Dual | Grand 600-cell |
Properties | Regular |
In geometry, the great grand stellated 120-cell or great grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,3,3}, one of 10 regular Schläfli-Hess 4-polytopes. It is unique among the 10 for having 600 vertices, and has the same vertex arrangement as the regular convex 120-cell.
It is one of four regular star polychora discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids, and the only one containing all three modifiers in the name.
H4 | A2 / B3 | A3 / B2 |
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Great grand stellated 120-cell, {5/2,3,3} | ||
[10] | [6] | [4] |
120-cell, {5,3,3} | ||
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.
The edges of the great grand stellated 120-cell are τ6 as long as those of the 120-cell core deep inside the polychoron, and they are τ3 as long as those of the small stellated 120-cell deep within the polychoron.