Great stellated 120-cell

Great stellated 120-cell
Orthogonal projection
Type	Schläfli-Hess polychoron
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	--

Orthogonal projection as a wireframe

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

It is one of four regular star polychora 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.

See also

• List of regular polytopes
• Convex regular 4-polytope - Set of convex regular polychoron
• 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)

External links

• Regular polychora
• 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