Thingiverse
Good Fibrations
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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
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
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