120-Cell Sections and Net

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The sections of the 120-cell (a four-dimensional regular polytope composed of 120 dodecahedral cells) are cut by three-dimensional hyperplanes parallel to one cell and intersecting sets of vertices. These sections progress from an initial cell at the "south pole" (Section VIII) to the "equator" (Section XIV), labeled as in the figures from Alicia Boole Stott's 1900 paper "On certain Series of Sections of the Regular Four-dimensional Hypersolids." Stott was the first to build models of these sections, using card stock. Sections VIII and IX are dodecahedra, Section X is an icosidodecahedron, and Section XIII is a rhombicosidodecahedron, but all files are scaled as sections of the 120-cell. The assembly of dodecahedra in the images represents a partial "net" for the 120-cell, constructed from 75 copies of Section VIII. The dodecahedral cell forms the "south pole" at the center, and the red cells around the periphery form the "equator." To complete the net, another copy of this partial net, excluding the "equatorial" cells, would have to be attached. The sections only go up to the equator; beyond Section XIV, the sections repeat in reverse order from XIII to VIII. The models are colored consistently: the cell at the "south pole" is uncolored, those around it are yellow, the next layers green, blue, and red, in that order. Each polygonal face is a section of a dodecahedral cell. Where faces shared by yellow cells and blue cells appear as pentagons in Section XI, a choice must be made for face color. Created after reading Coxeter's Regular Polytopes.