Geometry

Tetrahedra Tangle

1. The Tetrahedron

Meet the simplest 3D shape. It has 4 identical triangular faces, 4 vertices, and 6 edges. You can drag to rotate and scroll to zoom.

2. Face to Face

What happens when we attach an identical tetrahedron to one of its faces? The shape grows, but notice how the angles meet.

3. Branching Out

Now let's attach a new tetrahedron to every exposed face of the original shape. This is Iteration 2. The complexity begins to bloom.

4. Avoiding Intersections

If we keep adding tetrahedra (Iteration 4), we run into a problem: sometimes a new shape would intersect with an existing one. We must skip adding it there to preserve the structure's physical possibility.

5. Infinite Beauty

Explore the fractal-like beauty of higher iterations. At depth 20 or 50, the shape forms complex ridges, spikes, and valleys.

Colors each face with a distinct color from the palette, emphasizing the structural boundaries.

Tetrahedra: 1

Exposed Faces: 4