Discrete Examples
Three of the six regular 4-polytopes – 8-cell (tesseract), 24-cell, and 120-cell – can each be partitioned into disjoint great circle (regular polygon) rings of cells forming discrete Hopf fibrations of these polytopes. The tesseract partitions into two interlocking rings of four cubes each. The 24-cell partitions into four rings of six octahedrons each. The 120-cell partitions into twelve rings of ten dodecahedra each.
The 600-cell also partitions into 20 rings of 30 tetrahedra each in a very interesting, quasi-regular chain called the Boerdijk–Coxeter helix. When superimposed onto the 3-sphere curvature it becomes regular.
Read more about this topic: Hopf Fibration
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