Editing 24-cell (section)

==== 4-cell rings ====
Four unit-edge-length octahedra can be connected vertex-to-vertex along a common axis of length 4{{radic|2}}. The axis can then be bent into a square of edge length {{radic|2}}. Although it is possible to do this in a space of only three dimensions, that is not how it occurs in the 24-cell. Although the {{radic|2}} axes of the four octahedra occupy the same plane, forming one of the 18 {{radic|2}} great squares of the 24-cell, each octahedron occupies a different 3-dimensional hyperplane,{{Efn|Just as each face of a [[polyhedron]] occupies a different (2-dimensional) face plane, each cell of a [[polychoron]] occupies a different (3-dimensional) cell [[hyperplane]].{{Efn|name=hyperplanes}}}} and all four dimensions are utilized. The 24-cell can be partitioned into 6 such 4-cell rings (three different ways), mutually interlinked like adjacent links in a chain (but these [[Link (knot theory)|links]] all have a common center). An [[#Isoclinic rotations|isoclinic rotation]] in the great square plane by a multiple of 90° takes each octahedron in the ring to an octahedron in the ring.