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.

Great 120-cell
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
Symmetry group	H4, [3,3,5]
Dual	self-dual
Properties	Regular

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.

More information H4, - ...

Orthographic projections by Coxeter planes

H4	-	F4
[30]	[20]	[12]
H3	A2 / B3 / D4	A3 / B2
[10]	[6]	[4]

Close

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.

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

• Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder .
• H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26, Regular Star-polytopes, pp. 404–408)
• Klitzing, Richard. "4D uniform polytopes (polychora) o5o5/2o5x - gohi".

• Regular polychora Archived 2003-09-06 at the Wayback Machine
• Discussion on names
• Reguläre Polytope
• The Regular Star Polychora

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