These two sculptures highlight the edges of sets of intertwining rings related to Hopf fibrations within the four-dimensional 120-cell and 600-cell polychora.
Because the shapes exist in four-dimensional space, special mathematical techniques are required to visualize them. These sculptures are made using the cell-centered stereographic projection method to create three-dimensional “shadows” of the original four-dimensional shapes.
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. The lines in this sculpture outline the edges of six of the intertwining rings, for a total of 60 cells.
The 600-cell another of the six regular convex four-dimensional shapes. It is composed of 600 tetrahedral cells composed of twenty 30-cell great circle rings related to the Hopf fibrations. The lines in this sculpture outline the edges of five of the intertwining rings, for a total of 150 cells.
Both sculptures require strategic supports to print. A version of the 600-cell with partial supports is also provided, although you will need to add your own to support the base.
This project was inspired by the book "Visualizing Mathematics with 3D Printing" by Henry Segerman.
