Coxeter plane projections of 4-polytopes
In your harness4D geometry toolMIT
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.
What it takes and gives
- 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
Limits. 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.
Details
- Kind
- 4D geometry tool
- Engine
- Python 3.10 or later
- Files
- 11 files, 306.7 KB
- Licence
- MIT
- Declared effects
- reads files, runs commands, writes files
- Checked with
- Godot 4.7.2, gl_compatibility (opengl3, Mesa llvmpipe under Xvfb)
- Checks
- cli rebuilds example, gltf structure example, cli rebuilds example, cli example runs, godot loads example, preview render
- Techniques
- Coxeter element and Coxeter number, Coxeter plane as an eigenspace of (c + c^T)/2, Petrie polygon, reflection matrices of simple roots, Wythoff construction
- Tags
- 4d, coxeter plane, petrie polygon, projection, symmetry, svg, 600-cell, gltf
- Identity
library.supply.creative_originals.8cab5fdcd34bd8b7938ca74b.4386b0f15c2bc6e9- Version
4386b0f15c2bc6e9344a6cb480634a4b4050b57695ab53e17996e9231040e861
The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.
Related files
Uniform 4-polytopes by the Wythoff constructionIn your harness
600-cell from the binary icosahedral groupIn your harness
120-cell from its seven coordinate classesIn your harness
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