A vertex-first cross-section uses some hyperplane orthogonal to a line joining opposite vertices of one of the 24-cells.
Shifting this hyperplane halfway to one of the vertices (e.g. xi = 1/2) gives rise to a regular cubic honeycomb.
Shifting again, so the hyperplane intersects the vertex, gives another rhombic dodecahedral honeycomb but with new 24-cells (the former ones having shrunk to points).
Each cuboctahedron in this honeycomb is a maximal cross-section of a 24-cell whose center lies in the plane.
Shifting this hyperplane till it lies halfway between the center of a 24-cell and the boundary, one obtains a bitruncated cubic honeycomb.
Shifting again, so the hyperplane intersects the boundary of the central 24-cell gives a rectified cubic honeycomb again, the cuboctahedra and octahedra having swapped positions.
As the hyperplane sweeps through 4-space, the cross-section morphs between these two honeycombs periodically.If a 3-sphere is inscribed in each hypercell of this tessellation, the resulting arrangement is the densest known[note 1] regular sphere packing in four dimensions, with the kissing number 24.
Alternatively, the same sphere packing arrangement with kissing number 24 can be carried out with smaller 3-spheres of edge-length-diameter, by locating them at the centers and the vertices of the 24-cells.
In this case the central 3-sphere kisses 24 others at the centers of the cubical facets of the three tesseracts inscribed in the 24-cell.
(This is the unique body-centered cubic packing of edge-length spheres of the tesseractic honeycomb.)
They are geometrically identical to the regular form, but the symmetry differences can be represented by colored 24-cell facets.