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

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.

Orthogonal projection as a wireframe
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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
 
[30]
 
[20]
 
[12]
H3 A2 / B3 / D4 A3 / B2
 
[10]
 
[6]
 
[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

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References

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  • 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-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".
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