Baltor Get started

Gallery / 4D geometry

24-cell from the Hurwitz quaternion units

In your harness4D geometry toolMIT

Generate the 24-cell as the binary tetrahedral group (closure of two unit quaternions), split it into three inscribed 16-cells by coset, check self-duality, and write a coset-coloured wireframe glTF or a polytope JSON record.

Render of 24-cell from the Hurwitz quaternion units
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
closure, hurwitz_units, is_group, cosets, facet_normals, polytope, is_24cell, is_sixteen_cell and 6 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. Tubes are straight segments between projected vertices; under the stereographic projection the true edge images are circular arcs. Group closure compares elements after rounding to 8 decimals, so generators must be exact to that precision. The perspective projection refuses an eye inside the rotated 24-cell.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 244.8 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 24cell lines, preview render
Techniques
Schlafli symbol {3,4,3}, Hurwitz quaternions, binary tetrahedral group 2T of order 24, cosets of the quaternion group Q8, self-duality of the 24-cell
Tags
4d, 24-cell, icositetrachoron, polytope, quaternion, hurwitz units, binary tetrahedral group, self-dual
Identity
library.supply.creative_originals.cfce950cf1d6701cb5fac5bf.43aecd0902ac4012
Version
43aecd0902ac4012039778570e74ec9e089f62edbef9c199c28f4c1b94abd0c2

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

Something wrong with this item, its rights or its safety? Report it on the support page, or from your harness after a download.