🧪 Transcendent Space Perfect Space Simulation

What does a truly "perfect" space look like — one built from absolutely identical cells, packed with total order and not a single gap or overlap? This simulator renders the three convex solids known to tile 3D space exactly this way: the cube on a simple cubic lattice, the rhombic dodecahedron on a face-centred cubic lattice, and the truncated octahedron — Lord Kelvin's 1887 candidate for the minimal-surface partition of space — on a body-centred cubic lattice. Switch between cell shapes, dial the lattice out to thousands of cells, and drag the gap slider to watch a mathematically perfect honeycomb break apart into individually visible cells, while live readouts track each cell's volume, surface area and isoperimetric quotient — the precise sense in which Kelvin's cell is more efficient than a cube.