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geometry 4d

24-cell from the Hurwitz quaternion units

Generate the 24-cell as the binary tetrahedral group (closure of two unit quaternions), split it into three inscribed 16-cells by coset, check self-duality, and write a coset-coloured wireframe glTF or a polytope JSON record.

Recorded render of 24-cell from the Hurwitz quaternion units

What this component contains

  • ATTRIBUTION.md
  • LICENSE
  • README.md
  • component.json
  • example.gltf
  • fourd.py
  • icositetrachoron_24cell.py
  • preview.png
  • test_package.py
  • verification/native.json

How it works

Entry points
closure, hurwitz_units, is_group, cosets, facet_normals, polytope, is_24cell, is_sixteen_cell and 6 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_24cell_lines
  • preview_render

Limits to consider

Tubes are straight segments between projected vertices; under the stereographic projection the true edge images are circular arcs. Group closure compares elements after rounding to 8 decimals, so generators must be exact to that precision. The perspective projection refuses an eye inside the rotated 24-cell.