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geometry 4d

120-cell from its seven coordinate classes

Build the 120-cell from its coordinate rule (even permutations included), take its dodecahedral cells from the icosian directions, split its vertices into five inscribed 600-cells, and write a glTF of two linked rings of ten cells plus all edges.

Recorded render of 120-cell from its seven coordinate classes

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • fourd.py
  • hecatonicosachoron_120cell.py
  • preview.png
  • test_package.py
  • verification/native.json

How it works

Entry points
even_permutations, coordinate_classes, icosians, polytope, inscribed_600cells, is_600cell, cell_ring, meshes and 4 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_120cell_ortho
  • preview_render

Limits to consider

Edges are one-pixel LINES whose width depends on the viewer; only the twenty ring cells are solid. Building the polytope takes about half a second in CPython. Vertices are merged after rounding to 12 decimals and inscribed 600-cell orbits after rounding to 7, which suits the built-in coordinates but not arbitrary input.