Half of a 120-cell

thingiverse

This model is highlighted in figure 3.22 of Visualizing Mathematics with 3D Printing, which was a joint effort with Saul Schleimer. The 120-cell ranks as one of the six regular 4-dimensional polytopes, an achievement gained from projecting its edges radially onto the unit 3-sphere within four-dimensional space, then using stereographic projection to visualize it in three-dimensional space. The final step was eliminating half of the resulting design located in the hemi-3-sphere closest to the point of projection, making it feasible to print in our familiar 3D environment.