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Uniform 4-polytopes by the Wythoff construction

In your harness4D geometry toolMIT

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.

Render of Uniform 4-polytopes by the Wythoff construction
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

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

Limits. 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.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 148.8 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 runcinated 5cell, preview render
Techniques
Wythoff construction, Coxeter-Dynkin diagrams with ringed nodes, reflection group orbits, fundamental weights as facet normals, simple roots from the Cholesky factor of the Coxeter Gram matrix
Tags
4d, uniform polytope, wythoff construction, coxeter group, truncation, polytope, f-vector, gltf
Identity
library.supply.creative_originals.796b18746d54c0db2926fa16.3c3215e2faa948b5
Version
3c3215e2faa948b527e17aa08d31e986ec99d7e0944e0287ecb451a425ca2e60

The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.

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