120-Cell Sections and Net by Professortiz

Last crawled date: 3 years, 1 month ago

The sections of the 120-cell (a four-dimensional regular polytope built out of 120 dodecahedral cells) as cut by three-dimensional hyperplanes parallel to one cell and intersecting sets of vertices.
The sections go 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 herself was the first to build models of these sections, but hers were made from card stock. Sections VIII and IX are dodecahedra, Section X an icosidodecahedron, and Section XIII a rhombicosidodecahedron, but the files are all to scale as sections of the 120-cell.
The assemblage of dodecahedra shown in the images represents the a partial "net" for the 120-cell, built from 75 copies of Section VIII, with the dodecahedral cell forming the "south pole" at the center, and the red cells around the periphery forming 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 to the equator as well; beyond Section XIV, the sections would repeat in reverse order from XIII to VIII.
The models are all colored consistently, with the cell at the "south pole" being uncolored, those around it yellow, the next layers green, blue, and red, in that order. Each polygonal face is a section of a dodecahedral cell. Where the faces shared by the yellow cells and the blue cells appear as the pentagons in Section XI, a choice had to be made for face color.
Created after reading Coxeter's Regular Polytopes.