Editing 600-cell (section)

===== Squares =====
The [[16-cell#Helical construction|fibrations of the 16-cell]] include 3 fibrations of its 6 great squares: 3 fiber bundles of 2 great squares. The 2 Clifford parallel squares in each bundle are completely disjoint. Adjacent parallel squares are spanned by edges of other great squares.
Each fiber bundle delineates 2 helical rings of 8 tetrahedral cells each.
Each tetrahedral cell occupies only one cell ring in each of the 3 fibrations.
The tetrahedral cell contributes each of its 6 edges to a different square (contributing two opposite non-intersecting edges to each of the 3 fibrations), but contributes each edge to both of the two distinct cell rings in the fibration.

The 600-cell contains 75 16-cells, and can be seen (10 different ways) as a compound of 15 disjoint 16-cells.
It has 15 fibrations of its 450 great squares: 15 fiber bundles of 30 great squares. The 30 Clifford parallel squares in each bundle are completely disjoint. Adjacent parallel squares are spanned by edges of great decagons.{{Efn|name=equi-isoclinic squares}} Each fiber bundle delineates 30 cell-disjoint helical rings of 8 tetrahedral cells each.{{Efn|These are the {{radic|2}} tetrahedral cells of the 75 inscribed 16-cells, ''not'' the {{radic|0.𝚫}} tetrahedral cells of the 600-cell.|name=two different tetrahelixes}} 
The Hopf map of this fibration is the [[icosidodecahedron]], where the 30 vertices each lift to a bundle of great squares.{{Sfn|Sadoc|2001|p=577|loc=§2.4 Discretising the fibration for the {3, 3, 5} polytope: the four-fold screw axis}}
Each tetrahedral cell occupies only one of the 30 8-tetrahedron rings in each of the 15 fibrations.