120-Cell Sculpture: Two Solid Rings

This sculpture highlights two solid rings of cells related to Hopf fibrations within the four-dimensional 120-cell 4-polytope.

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells and can be partitioned into twelve 10-cell great circle rings related to the Hopf fibrations.

You can count the 10 cells in the ring of dodecahedra that arc over the top. But where is the other ring? The other ring is composed of the line of 9 horizontal cells. The tenth cell in this ring is infinitely large, so you are inside it. There’s four-dimensional geometry for you.

Because the shapes exist in four-dimensional space, special mathematical techniques are required to visualize them. This sculpture is made using the cell-centered stereographic projection method to create three-dimensional “shadows” of the original four-dimensional shapes.

The file is provided plain and with custom central supports.

See here for more related 120 Cell projects: 120 Cell Study: https://thangs.com/mythangs/file/63695 120 Cell Rings: https://thangs.com/mythangs/file/63697 120 Cell Polychora Planter: https://thangs.com/mythangs/file/64633 120 Cell Sculpture: Two Solid Rings: https://thangs.com/mythangs/file/64702 120 Cell Sculpture: Six Intertwining Rings: https://thangs.com/mythangs/file/63899 120 Cell Sculpture: Two Intertwining Rings: https://thangs.com/mythangs/file/64700 120 Cell Platter: https://thangs.com/mythangs/file/26199