This print-in-place “120-cell Linked Rings” sculpture offers a tactile way to explore and appreciate the four-dimensional 120-cell.

See here for video: https://youtu.be/87hM1U-2sWY

The 120-cell is one of six regular convex four-dimensional shapes. It is composed of 120 dodecahedral cells.

Because the shape exists in four-dimensional space, special mathematical techniques are required to visualize it. This sculpture is made using the cell-centered stereographic projection method to create a three-dimensional “shadow” of the original four-dimensional shape.

Even these “simplified” three-dimension shapes are difficult to fully understand, so it is helpful to deconstruct them further.

The 120-cell can be partitioned into twelve 10-cell great circle rings.

This sculpture contains 60 dodecahedral cells clustered in to six of these 10-cell rings, representing half of the full 120-cell. Because five of the rings wrap around and hide the sixth ring, it is difficult to see their relative positioning. The “120-cell Fused Rings” object contains all 60 cells, but you can only see the outer 50.

In the “120-cell Linked Rings” object, the six rings have been separated and small supports have been added between the rings to allow printing with a well-calibrated FDM printer. Once printed, the rings can be separated by gently twisting them apart to reveal the inner ring.

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