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Schlegel diagrams of convex 4-polytopes

In your harness4D geometry toolMIT

Project a convex 4-polytope from a point just outside one cell onto that cell, so all other cells nest inside it, and write the diagram as a glTF wireframe with the outer cell as a translucent shell. Built-in regular polytopes or any polytope JSON record.

Render of Schlegel diagrams of convex 4-polytopes
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
load_polytope, eye_point, project, outer_faces, inside_outer_cell, depth, meshes, export and 3 more
Outputs
example.gltf
Coordinates
3D coordinates in the chosen cell's hyperplane basis, origin at the cell centroid; Godot/glTF +Y up

Limits. The polytope must be convex and its record must list cells (the eye position is computed from the cell hyperplanes). The eye sits halfway to the nearest other cell hyperplane; other choices change the nesting depth but not the combinatorics. LINES are one pixel wide in most viewers; the shell relies on the viewer's alpha sorting.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 216.7 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 schlegel 120cell, preview render
Techniques
Schlegel diagram, central projection onto a facet hyperplane, viewpoint inside the region beyond exactly one facet, Coxeter group orbits for regular polytopes
Tags
4d, schlegel diagram, projection, polytope, 120-cell, nested cells, gltf
Identity
library.supply.creative_originals.fd41f4ec76d0c04e319908c6.83ca51c8b065501c
Version
83ca51c8b065501ce53f5096a85f60eb1d5529bf772d28f7d3e418b3691aa931

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

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