AgentStudiosSign in ↗
← All examples

geometry 4d

Uniform 4-polytopes by the Wythoff construction

Generate the uniform polytope of a Coxeter group (A4, B4, D4, F4, H4) and a ringed diagram with unit edges: vertices, edges, faces, cells and cell types, written as exploded cells coloured by cell type, a wireframe glTF or a polytope JSON record.

Recorded render of Uniform 4-polytopes by the Wythoff construction

What this component contains

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

How it works

Entry points
parse_rings, name, construct, cell_types, edge_lengths, mesh, export, invariants and 2 more
Outputs
example.gltf
Coordinates
x, y, z, w in the frame of the group's simple roots (axis-aligned for B4 and F4); 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_runcinated_5cell
  • preview_render

Limits to consider

Ringings whose orbit exceeds 1500 vertices are refused (most H4 forms beyond the truncated 600-cell). Finding the cells scans every image of the four fundamental weights, which takes seconds for the larger H4 forms in CPython. Snub and other non-Wythoffian uniform polytopes are out of scope. A4, D4 and H4 coordinates come from a Cholesky factor of the Gram matrix, so their orientation is not axis-aligned.