Grand 600-cell

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Grand 600-cell
Ortho solid 015-uniform polychoron 33p-t0.png
Orthogonal projection
Type Schläfli-Hess polychoron
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 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png
Symmetry group H4, [3,3,5]
Dual Great grand stellated 120-cell
Properties Regular
Orthogonal projection of wireframe

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

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.

Related polytopes[edit]

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 polychora, 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.

See also[edit]


  • Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder [1].
  • H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26, Regular Star-polytopes, pp. 404–408)

External links[edit]