Grand 120-cell

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.

Grand 120-cell

Orthogonal projection
TypeSchläfli-Hess polytope
Cells120 {5,3}
Faces720 {5}
Edges720
Vertices120
Vertex figure{3,5/2}
Schläfli symbol{5,3,5/2}
Coxeter-Dynkin diagram
Symmetry groupH4, [3,3,5]
DualGreat stellated 120-cell
PropertiesRegular

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.

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]

With its dual, it forms the compound of grand 120-cell and great stellated 120-cell.

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

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 .
  • 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) o5o3o5/2x - gahi".
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