Great 120-cell

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
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

[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

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. 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".

External links

  • Regular polychora Archived 2003-09-06 at the Wayback Machine
  • Discussion on names
  • Reguläre Polytope
  • The Regular Star Polychora
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Convex
5-cell8-cell16-cell24-cell120-cell600-cell
  • {3,3,3}
  • pentachoron
  • 4-simplex
  • {4,3,3}
  • tesseract
  • 4-cube
  • {3,3,4}
  • hexadecachoron
  • 4-orthoplex
  • {3,4,3}
  • icositetrachoron
  • octaplex
  • {5,3,3}
  • hecatonicosachoron
  • dodecaplex
  • {3,3,5}
  • hexacosichoron
  • tetraplex
Star
icosahedral
120-cell		small
stellated
120-cell		great
120-cell		grand
120-cell		great
stellated
120-cell		grand
stellated
120-cell		great grand
120-cell		great
icosahedral
120-cell		grand
600-cell		great grand
stellated 120-cell
  • {3,5,5/2}
  • icosaplex
  • {5/2,5,3}
  • stellated dodecaplex
  • {5,5/2,5}
  • great dodecaplex
  • {5,3,5/2}
  • grand dodecaplex
  • {5/2,3,5}
  • great stellated dodecaplex
  • {5/2,5,5/2}
  • grand stellated dodecaplex
  • {5,5/2,3}
  • great grand dodecaplex
  • {3,5/2,5}
  • great icosaplex
  • {3,3,5/2}
  • grand tetraplex
  • {5/2,3,3}
  • great grand stellated dodecaplex


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