An interactive visualizer for Goldberg polyhedra on the sphere, exploring degrees of freedom under strict symmetry and geometric constraints.

The goal of this project is to visualize degrees of freedom in various (Goldberg) polyhedra while preserving key properties:

1. Icosahedral symmetry: Preserves full 3D icosahedral symmetry.
2. 120° rotational symmetry: Rotational symmetry around a single icosahedral face.
3. "Left-right" symmetry: Reflection/mirror symmetry around a single icosahedral face.
4. "On-sphere" (inscribable): Vertices are constrained to lie on the unit sphere (distance from origin = 1), enforced by using a spherical coordinate system.

Under these constraints, the project investigates how deforming the polyhedra affects properties like edge-length equality (equilateral faces) and face planarity.

• (1, 0) Dodecahedron: The base case. Has 0 degrees of freedom. Used for layout debugging.
• (1, 1) Truncated Icosahedron: Has 1 degree of freedom ($t_1$, defining the amount of truncation).
• (2, 0) Goldberg: Has 1 degree of freedom ($t_1$). Setting it to ~0.42 results in an equilateral, planar, on-sphere Goldberg polyhedron.

• Anything from 2024 and before is painstakingly hand-crafted.
• Commits from 2026 and later (yes there was an almost two year gap) are mostly AI-assisted.

• Implement Goldberg (2, 2) Subdivision.
• Implement Goldberg (4, 4) Subdivision.