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120-cell from its seven coordinate classes

In your harness4D geometry toolMIT

Build the 120-cell from its coordinate rule (even permutations included), take its dodecahedral cells from the icosian directions, split its vertices into five inscribed 600-cells, and write a glTF of two linked rings of ten cells plus all edges.

Render of 120-cell from its seven coordinate classes
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
even_permutations, coordinate_classes, icosians, polytope, inscribed_600cells, is_600cell, cell_ring, meshes and 4 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

Limits. Edges are one-pixel LINES whose width depends on the viewer; only the twenty ring cells are solid. Building the polytope takes about half a second in CPython. Vertices are merged after rounding to 12 decimals and inscribed 600-cell orbits after rounding to 7, which suits the built-in coordinates but not arbitrary input.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 211.0 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 120cell ortho, preview render
Techniques
Schlafli symbol {5,3,3}, coordinates of the 120-cell from even permutations with the golden ratio, icosians as cell directions of the dual 600-cell, orbits of left quaternion multiplication, rings of ten cells along a great decagon
Tags
4d, 120-cell, hecatonicosachoron, dodecahedral cells, polytope, icosians, golden ratio, gltf
Identity
library.supply.creative_originals.7da92872f36eb38cae6b60e6.8822f892344227a2
Version
8822f892344227a2c106c90a333760cf5512b49eb3acf5fe4622635e79622a47

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

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