Grand 120-cell

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Grand 120-cell
Ortho solid 009-uniform polychoron 53p-t0.png
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 CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.pngCDel rat.pngCDel d2.pngCDel node.png
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.

Related polytopes[edit]

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
600-cell graph H4.svg
[30]
600-cell t0 p20.svg
[20]
600-cell t0 F4.svg
[12]
H3 A2 / B3 / D4 A3 / B2
600-cell t0 H3.svg
[10]
600-cell t0 A2.svg
[6]
600-cell t0.svg
[4]

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

See also[edit]

References[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) o5o3o5/2x - gahi".

External links[edit]