Grand 120-cell

Orthogonal projection
Type Schläfli-Hess polytope
Cells 120 {5,3}
Faces 720 {5}
Edges 720
Vertices 120
Vertex figure {3,5/2}
Schläfli symbol {5,3,5/2}
Coxeter-Dynkin diagram
Symmetry group H4, [3,3,5]
Dual Great stellated 120-cell
Properties Regular

In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes.

It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.

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It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell.

Orthographic projections by Coxeter planes
H4 - F4
 
[30]
 
[20]
 
[12]
H3 A2 / B3 / D4 A3 / B2
 
[10]
 
[6]
 
[4]

It could be seen as another 4D analogue of the three-dimensional great dodecahedron due to being a pentagonal polytope with enlarged facets.

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) o5o3o5/2x - gahi".
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