Great grand stellated 120-cell

Great grand stellated 120-cell

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
A Zome model

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.

With its dual, it forms the compound of great grand stellated 120-cell and grand 600-cell.

Images

Coxeter plane images
H4 A2 / B3 A3 / B2
Great grand stellated 120-cell, {5/2,3,3}

[10] [6] [4]
120-cell, {5,3,3}

As a stellation

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.