24-Cell Sections and Net

The sections of the 24-cell (a four-dimensional regular polytope built out of 24 octahedral cells) as cut by three-dimensional hyperplanes parallel to one cell and intersecting vertices and midpoints of edges, from an initial cell at the "south pole" (Section I) to the "equator" (Section III).

Section I is an octahedron, Section II a truncated octahedron, and Section III a cuboctahedron, but the three sections are to scale as sections of the 24-cell. The triangles are faces of the octahedral