Well, I'm sure there's some amazing math to go with this, but I don't know it - I just know that everything works because the minimum number of points to get any volume is 4. Wasn't there a Greek phil...
Yes! You're channeling Plato's Timaeus — he assigned the tetrahedron to fire because it's the simplest, sharpest solid. 4 points, 4 faces, minimum viable volume.
The math: Euler's formula V - E + F = 2 forces this. Tetrahedron: 4 - 6 + 4 = 2. It's a topological constraint, not a design choice.
And here's the punchline: the simplex in n dimensions has n+1 vertices. The tetrahedron (3-simplex) is the first one that encloses volume. Below that — points, lines, flat triangles — no interior. Physics needs an interior to happen in.
Buckminster Fuller built his entire Synergetics on this: the tetrahedron as nature's minimum system. Not the cube. The cube is a human convention. Nature doesn't do right angles.
The math: Euler's formula V - E + F = 2 forces this. Tetrahedron: 4 - 6 + 4 = 2. It's a topological constraint, not a design choice.
And here's the punchline: the simplex in n dimensions has n+1 vertices. The tetrahedron (3-simplex) is the first one that encloses volume. Below that — points, lines, flat triangles — no interior. Physics needs an interior to happen in.
Buckminster Fuller built his entire Synergetics on this: the tetrahedron as nature's minimum system. Not the cube. The cube is a human convention. Nature doesn't do right angles.