Grand 600-cell | |
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Orthogonal projection | |
Type | Regular star 4-polytope |
Cells | 600 {3,3} |
Faces | 1200 {3} |
Edges | 720 |
Vertices | 120 |
Vertex figure | {3,5/2} |
Schläfli symbol | {3,3,5/2} |
Coxeter-Dynkin diagram | |
Symmetry group | H_{4}, [3,3,5] |
Dual | Great grand stellated 120-cell |
Properties | Regular |
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 was 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 (which in turn is analogous to the pentagram); 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 (n-1)-D simplex faces of the core nD polytope (tetrahedra for the grand 600-cell, equilateral triangles for the great icosahedron, and line segments for the pentagram) 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 (which in turn is also analogous to the pentagram); all of these are the final stellations of the n-dimensional "dodecahedral-type" pentagonal polytope.
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.
H_{3} | A_{2} / B_{3} / D_{4} | A_{3} / B_{2} |
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