Small stellated 120-cell

It has the same edge arrangement as the great grand 120-cell, and also shares its 120 vertices with the 600-cell and eight other regular star 4-polytopes. It may also be seen as the first stellation of the 120-cell. In this sense it could be seen as analogous to the three-dimensional small stellated dodecahedron, which is the first stellation of the dodecahedron. Indeed, the small stellated 120-cell is dual to the icosahedral 120-cell, which could be taken as a 4D analogue of the great dodecahedron, dual of the small stellated dodecahedron.

The edges of the small stellated 120-cell are τ² as long as those of the 120-cell core inside the 4-polytope.

Orthographic projections by Coxeter planes

H3	A2 / B3 / D4	A3 / B2

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

• 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) o3o5o5/2x - sishi".

• Regular polychora
• Discussion on names
• Reguläre Polytope
• The Regular Star Polychora
• Zome Model of the Final Stellation of the 120-cell
• The First Stellation of the 120-cell, A Zome Model