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geometry 4d

5-cell from the standard simplex of R5

Place the regular 4-simplex in 4D through the Helmert basis, with barycentric coordinates, uniform interior sampling and a permutation symmetry check, and write exploded cells, a wireframe glTF or a polytope JSON record.

Recorded render of 5-cell from the standard simplex of R5

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • fourd.py
  • preview.png
  • simplex_5cell.py
  • test_package.py
  • verification/native.json

How it works

Entry points
helmert_basis, vertices, polytope, barycentric, contains, sample_points, symmetry_count, dihedral_angle and 5 more
Outputs
example.gltf
Coordinates
x, y, z, w (Helmert coordinates of R5); 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_5cell_tubes
  • preview_render

Limits to consider

The exploded view shrinks each projected cell toward its own projected centroid, which is a display choice, not a geometric operation in 4D. Sampling uses Python's random module with a fixed seed, so it is reproducible but not cryptographic. Under the stereographic projection, flat faces between projected vertices only approximate the curved images of the cells.