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geometry 4d

Coxeter plane projections of 4-polytopes

Find the plane in which the Coxeter element of A4, B4, F4 or H4 turns by 2 pi/h and project a regular or Wythoff 4-polytope onto it, giving the h-fold symmetric drawing with its concentric rings, written as SVG or as a flat glTF.

Recorded render of Coxeter plane projections of 4-polytopes

What this component contains

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

How it works

Entry points
reflection_matrix, coxeter_element, element_order, coxeter_plane, named_polytope, project, rings, is_symmetric and 6 more
Outputs
example.gltf, example.svg
Coordinates
2D Coxeter plane coordinates; in the glTF the drawing lies in the xy plane (z = 0), scaled to radius 1

Recorded checks

godot 4.7.2.stable.official.ed1daf0bf

  • cli_rebuilds_example
  • gltf_structure_example
  • cli_rebuilds_example
  • cli_example_runs
  • godot_loads_example
  • preview_render

Limits to consider

Vertices come from Coxeter group orbits and are capped at 3000; edges join vertices at distance 1, which is the edge length of every Wythoff polytope. Ring counts group points by radius, so two rings of h points at one radius count as one ring of 2h (the 120-cell shows 12 radii for 20 orbits). The drawing is orthographic: vertices may coincide in the plane for some ringings.