Great stellated 120-cell

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

Great stellated 120-cell

Orthogonal projection
TypeSchläfli-Hess polytope
Cells120 {5/2,3}
Faces720 {5/2}
Edges720
Vertices120
Vertex figure{3,5}
Schläfli symbol{5/2,3,5}
Coxeter-Dynkin diagram
Symmetry groupH4, [3,3,5]
DualGrand 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 grand 600-cell, icosahedral 120-cell, and the same face arrangement as the grand stellated 120-cell.

Orthographic projections by Coxeter planes
H3 A2 / B3 / D4 A3 / B2

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

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 .
  • 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 - gishi".
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