Nicolas Scheer
home / projects / hyperforge
2026Blender add-onv1 done

hyperforge

Blender add-on to generate, animate and visualize the 6 regular 4-dimensional polytopes (tesseract, 120-cell, 600-cell...).

6 regular 4D polytopes and 3 quaternion Julia sets

5-cell (simplex) — 5 vertices, 10 edges
5-cell (simplex) — 5 vertices, 10 edges
8-cell (tesseract) — 16 vertices, 32 edges
8-cell (tesseract) — 16 vertices, 32 edges
16-cell (cross-polytope) — 8 vertices, 24 edges
16-cell (cross-polytope) — 8 vertices, 24 edges
24-cell — 24 vertices, 96 edges
24-cell — 24 vertices, 96 edges
120-cell — 600 vertices, 1200 edges
120-cell — 600 vertices, 1200 edges
600-cell — 120 vertices, 720 edges
600-cell — 120 vertices, 720 edges
Quaternion Julia set — c = (-0.2, 0.8, 0, 0)
Quaternion Julia set — c = (-0.2, 0.8, 0, 0)
Quaternion Julia set — c = (-0.162, 0.163, 0.56, -0.599)
Quaternion Julia set — c = (-0.162, 0.163, 0.56, -0.599)
Quaternion Julia set — c = (-0.45, -0.447, 0.181, 0.306)
Quaternion Julia set — c = (-0.45, -0.447, 0.181, 0.306)

3D viewport — real mesh exported from the project, navigable with the mouse

tesseract (8-cell) · orbit
glisser pour tourner · molette pour zoomer

Problem

Make geometric objects of dimension higher than 3 — normally confined to abstract computation — manipulable by an artist, useful for morphing effects or non-Euclidean visuals.

Approach

Exact algebraic generation of each polytope's vertices (the 600-cell via even permutations of the golden ratio, the 120-cell by duality), 4D rotation composed of 6 elementary rotations per axis plane, and two visualization modes: slicing by a moving hyperplane and 4D→3D perspective projection. Pure NumPy math modules, testable outside Blender, decoupled from the UI/Geometry Nodes integration. The same 4D foundation (quaternions = 4-dimensional vectors) is also used to extract quaternion Julia sets by isosurface (marching cubes on a smoothed escape potential), outside the polytope framework.

Results

6 working polytopes, 2 visualization modes, 3 LOD levels, keyframe animation — add-on delivered in one focused development session.

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