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600-cell from the binary icosahedral group

In your harness4D geometry toolMIT

Generate the 600-cell as the 120 icosians (closure of two unit quaternions), find its faces and cells as cliques, split it into 12 Hopf decagons and 5 inscribed 24-cells by cosets, and write a glTF with the decagons as coloured tubes.

Render of 600-cell from the binary icosahedral group
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
closure, icosians, order, clique_polytope, polytope, left_cosets, hopf_decagons, is_regular_decagon and 7 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. Only the 120 Hopf decagon edges are tubes; the other 600 edges are one-pixel LINES, whose width depends on the viewer. The quaternion 1 is a vertex at the stereographic pole, so the stereographic projection needs a rotation that moves it away (the default does). Group closure merges elements after rounding to 8 decimals.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 299.2 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 600cell ortho, preview render
Techniques
Schlafli symbol {3,3,5}, binary icosahedral group 2I with s^3 = t^5 = (st)^2 = -1, icosians, cosets of a cyclic subgroup as Hopf fibres (Clifford parallel great circles), cosets of the binary tetrahedral group as inscribed 24-cells, cliques of the edge graph as faces and cells
Tags
4d, 600-cell, hexacosichoron, icosians, binary icosahedral group, hopf fibration, clifford parallels, polytope
Identity
library.supply.creative_originals.63cbe373b3ae30d809ea75ab.07018545552e4757
Version
07018545552e475789e74f6ae176ef895d2be44e840a81b2a3870a6172cb3590

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

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