Thingiverse

Clifford Sculptures

by DaveMakesStuff

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These sculptures are derived from the Clifford parallel geodesics of the cell-centered stereographic projection of the four-dimensional 600-cell.

See here for video: https://youtu.be/MTMeT03aBJ0

See here for stable downloads:
https://thangs.com/mythangs/file/28272
https://thangs.com/mythangs/file/28273
https://thangs.com/mythangs/file/28271

The 600-cell is a stunningly beautiful regular 4-polytope, but its beauty is nearly impossible to appreciate because, well, we can only perceive three dimensions!

One way to deconstruct and appreciate the 600-cell is to understand it in terms of geodesic great circles. The 600-cell is made up of 72 great decagons. The 72 great decagons can be divided into 6 sets of 12 non-intersecting Clifford parallel geodesics, such that only one decagonal great circle in each set passes through each vertex, and the 12 decagons in each set reach all 120 vertices.

When exploring or printing these sculptures, I encourage you to orient to the geome

4-polytope BoerdijkCoxeter circle Clifford Clifford geodesics Fourth Dimension geodesic math math art polychora polychoron polyhedra polyhedron sculpture sculptures tetrahedral tetrahedron 4-polytope BoerdijkCoxeter circle Clifford Clifford geodesics Fourth Dimension geodesic math math art polychora polychoron polyhedra polyhedron sculpture sculptures tetrahedral tetrahedron

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Thingiverse

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