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Gallery / 4D geometry

Duoprisms as products of two polygons

In your harness4D geometry toolMIT

Build any {p}x{q} duoprism exactly (pq vertices, two rings of prisms), with unit-edge or equal radii, check its counts and volume against the product formulas, and write exploded prisms, a wireframe glTF or a polytope JSON record.

Render of Duoprisms as products of two polygons
The render its check recorded in Godot 4.7.2, 256 by 256 pixels.

What it takes and gives

Entry points
radii, polytope, polygon_area, expected_counts, is_uniform, tesseract_check, mesh, export and 3 more
Outputs
example.gltf
Coordinates
x, y, z, w (p-gon in xy, q-gon in zw); projected to Godot/glTF +Y up

Limits. p times q is capped at 4096 in the CLI. The exploded view shrinks each projected prism toward its own projected centroid, a display choice. The perspective projection refuses an eye inside the rotated duoprism; flat faces under the stereographic projection approximate curved cell images.

Details

Kind
4D geometry tool
Engine
Python 3.10 or later
Files
10 files, 144.0 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 duoprism 3 12, preview render
Techniques
Cartesian product of polygons (duoprism), f-vector of a product polytope, hypervolume of a product as the product of areas, uniform polygon radius 1/(2 sin(pi/n))
Tags
4d, duoprism, product polytope, prism ring, polygon, clifford torus, polytope, gltf
Identity
library.supply.creative_originals.ec56c46db2447978d39ea24a.37fdc54f95829033
Version
37fdc54f95829033844e00b45d5f1dce6a871b5c5a9e0ccaac80a9d096fcc8cd

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

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