Great 120-cell

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Great 120-cell
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 CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.pngCDel 5.pngCDel node.png
Symmetry group H4, [3,3,5]
Dual self-dual
Properties Regular
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[edit]

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
600-cell graph H4.svg
600-cell t0 p20.svg
600-cell t0 F4.svg
H3 A2 / B3 / D4 A3 / B2
600-cell t0 H3.svg
600-cell t0 A2.svg
600-cell t0.svg

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. With itself, it can form the compound of two great 120-cells.

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)
  • Klitzing, Richard. "4D uniform polytopes (polychora) o5o5/2o5x - gohi".

External links[edit]