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Gallery / 4D geometry

5-cell from the standard simplex of R5

In your harness4D geometry toolMIT

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.

Render of 5-cell from the standard simplex of R5
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

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

Limits. 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.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 137.7 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 5cell tubes, preview render
Techniques
Schlafli symbol {3,3,3}, Helmert orthonormal basis of the sum-zero hyperplane, barycentric coordinates, Dirichlet(1,...,1) sampling by sorted uniform spacings, regular simplex dihedral angle arccos(1/n)
Tags
4d, 5-cell, simplex, pentachoron, polytope, barycentric, helmert basis, gltf
Identity
library.supply.creative_originals.d046d4375177a29262227b27.c91fc2b93de3beea
Version
c91fc2b93de3beea55ef2e91cfbb0e3d259ce7050126d3889511257e9e6f5c8f

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

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