Great stellated 120-cell

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

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.

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

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

• 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 [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 - gishi".

External links

• Regular polychora Archived 2003-09-06 at the Wayback Machine
• Discussion on names
• Reguläre Polytope
• The Regular Star Polychora
• Paper model of 3D cross-section of Great Stellated 120-cell created using nets generated by Stella4D software