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Tesseract from 4-bit vertex labels

In your harness4D geometry toolMIT

Build the tesseract exactly (edges, square faces and cubic cells from bit patterns), rotate it in any of the six planes and write a projected wireframe glTF or a polytope JSON record. Also gives its Gray code cycle and inscribed 16-cells.

Render of Tesseract from 4-bit vertex labels
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
vertices, polytope, gray_cycle, is_hamiltonian_cycle, half_tesseracts, is_sixteen_cell, wireframe, export and 3 more
Outputs
example.gltf
Coordinates
x, y, z, w; projected to Godot/glTF +Y up

Limits. Tubes are straight segments between projected vertices, so under the stereographic projection they are chords, not the circular arcs that are the true images of great-circle edges. The perspective projection refuses an eye inside the rotated object. Depth colour is linear in the rotated w coordinate and is not physically based.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 186.0 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 tesseract lines, preview render
Techniques
Schlafli symbol {4,3,3}, hypercube as the product of four intervals, reflected binary Gray code, demitesseract (alternated tesseract) is the 16-cell, central perspective projection from a 4D eye point
Tags
4d, tesseract, hypercube, 8-cell, polytope, gltf, wireframe, gray code
Identity
library.supply.creative_originals.6b11b1b4b6e77fcacc73e9df.1396715b484b7b99
Version
1396715b484b7b99a29becc02c9fbd1516479cca93488e1c0b0095fa26c8c958

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

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