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geometry 4d

600-cell from the binary icosahedral group

Generate the 600-cell as the 120 icosians (closure of two unit quaternions), find its faces and cells as cliques, split it into 12 Hopf decagons and 5 inscribed 24-cells by cosets, and write a glTF with the decagons as coloured tubes.

Recorded render of 600-cell from the binary icosahedral group

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • fourd.py
  • hexacosichoron_600cell.py
  • preview.png
  • test_package.py
  • verification/native.json

How it works

Entry points
closure, icosians, order, clique_polytope, polytope, left_cosets, hopf_decagons, is_regular_decagon and 7 more
Outputs
example.gltf
Coordinates
x, y, z, w with the quaternion a + bi + cj + dk at (b, c, d, a); projected to Godot/glTF +Y up

Recorded checks

godot 4.7.2.stable.official.ed1daf0bf

  • cli_rebuilds_example
  • gltf_structure_example
  • cli_example_runs
  • cli_example_gltf_structure
  • godot_loads_example
  • godot_loads_cli_600cell_ortho
  • preview_render

Limits to consider

Only the 120 Hopf decagon edges are tubes; the other 600 edges are one-pixel LINES, whose width depends on the viewer. The quaternion 1 is a vertex at the stereographic pole, so the stereographic projection needs a rotation that moves it away (the default does). Group closure merges elements after rounding to 8 decimals.