Great 120-cell

Great 120-cell
File:Ortho solid 008-uniform polychoron 5p5-t0.png Orthogonal projection
Type	Schläfli-Hess polytope
Cells	120 {5,5/2}
Faces	720 {5}
Edges	720
Vertices	120
Vertex figure	{5/2,5}
Schläfli symbol	{5,5/2,5}
Coxeter-Dynkin diagram	Template:CDD
Symmetry group	H4, [3,3,5]
Dual	self-dual
Properties	Regular

File:Schläfli-Hess polychoron-wireframe-3.png

Orthogonal projection as a wireframe

In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,5}. 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.

Orthographic projections by Coxeter planes

H4	-	F4
File:600-cell graph H4.svg [30]	File:600-cell t0 p20.svg [20]	File:600-cell t0 F4.svg [12]
H3	A2 / B3 / D4	A3 / B2
File:600-cell t0 H3.svg [10]	File:600-cell t0 A2.svg [6]	File:600-cell t0.svg [4]

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 [1].
• H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. Template:ISBN.
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Template:ISBN (Chapter 26, Regular Star-polytopes, pp. 404–408)
• Template:KlitzingPolytopes

External links

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