16-cell from signed axes

In your harness4D geometry toolMIT

Build the 16-cell exactly from signed coordinate axes (cells are the 16 sign vectors), check its cocktail party edge graph and its duality with the tesseract, and write exploded cells, a wireframe glTF or a polytope JSON record.

Render of 16-cell from signed axes — The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points: vertices, polytope, is_cocktail_party, tesseract_cell_centres, apex_cells, mesh, export, invariants and 2 more
Outputs: example.gltf
Coordinates: x, y, z, w; projected to Godot/glTF +Y up

Limits. The exploded view shrinks each projected cell toward its own projected centroid, a display choice. Flat faces under the stereographic projection approximate curved cell images. The perspective projection refuses an eye inside the rotated 16-cell.

Details

Kind: 4D geometry tool
Engine: Python 3.10 or later
Files: 10 files, 137.8 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 example runs, cli example gltf structure, godot loads example, godot loads cli 16cell tubes, preview render
Techniques: Schlafli symbol {3,3,4}, cross-polytope (orthoplex) from signed unit vectors, cocktail party graph K_{2,2,2,2}, duality of the tesseract and the 16-cell, bipyramid over the octahedron
Tags: 4d, 16-cell, cross-polytope, orthoplex, hexadecachoron, polytope, dual, gltf
Identity: library.supply.creative_originals.abe1a9da658a94664a11a083.e8d9be4c5de9c37c
Version: e8d9be4c5de9c37c43134c43a4a7ba4e246928cd6eae43cb1c21a6539ed335a6

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16-cell from signed axes

What it takes and gives

Details

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