Small stellated 120-cell

Small stellated 120-cell
Orthogonal projection
Type	Schläfli-Hess polytope
Cells	120 {5/2,5}
Faces	720 {5/2}
Edges	1200
Vertices	120
Vertex figure	{5,3}
Schläfli symbol	{5/2,5,3}
Coxeter-Dynkin diagram
Symmetry group	H4, [3,3,5]
Dual	Icosahedral 120-cell
Properties	Regular

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

Related polytopes

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.^[1] 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

See also

• 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

References

1. Conrad, J.; Chamberland, C.; Breuckmann, N. P.; Terhal, B. M. (2018). "The small stellated dodecahedron code and friends". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2123): 20170323. Bibcode:2018RSPTA.37670323C. doi:10.1098/rsta.2017.0323. ISSN 1364-503X. PMC 5990658. PMID 29807900.

• 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-Strauss, 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".

External links

• 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