Grand 600-cell
In geometry, the grand 600-cell or grand polytetrahedron is a regular star 4-polytope with Schläfli symbol. 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.
The grand 600-cell can be seen as the four-dimensional analogue of the great icosahedron ; both of these are the only regular n-dimensional star polytopes which are derived by performing stellational operations on the pentagonal polytope which has simplectic faces. It can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of said -D simplex faces of the core nD polytope until the figure regains regular faces.
The Grand 600-cell is also dual to the great grand stellated 120-cell, mirroring the great icosahedron's duality with the great stellated dodecahedron ; all of these are the final stellations of the n-dimensional "dodecahedral-type" pentagonal polytope.Related polytopes
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.
With its dual, it forms the compound of great grand stellated 120-cell and grand 600-cell.
