Great 120-cell explained

bgcolor=#e7dcc3 colspan=2	Great 120-cell
bgcolor=#ffffff align=center colspan=2	Orthogonal projection
Type	Schläfli-Hess polytope
Cells	120
Faces	720
Edges	720
Vertices	120
Vertex figure
Schläfli symbol
Coxeter-Dynkin diagram
Symmetry group	H4, [3,3,5]
Dual	self-dual
Properties	Regular

In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol . It is one of 10 regular Schläfli-Hess polytopes. It is one of the two such polytopes that is self-dual.

Related polytopes

It has the same edge arrangement as the 600-cell, icosahedral 120-cell as well as the same face arrangement as the grand 120-cell.

Due to its self-duality, it does not have a good three-dimensional analogue, but (like all other star polyhedra and polychora) is analogous to the two-dimensional pentagram.

See also

• List of regular polytopes
• Convex regular 4-polytope
• Kepler-Poinsot solids regular star polyhedron
• Star polygon regular star polygons

References

• Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=ABN8623.0001.001.
• H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. .
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26, Regular Star-polytopes, pp. 404 - 408)

External links

• Regular polychora
• Discussion on names
• Reguläre Polytope
• The Regular Star Polychora