🧊 Spatial Lab 3D — Platonic Solids & Cross-Section Explorer

This 3D companion swaps the flat, decorative link hub of the original "Spatial Lab" page for a genuine WebGL solid-geometry lab: choose from the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) or a torus, and every readout — vertex, edge and face count, Euler characteristic, volume and surface area — is computed from exact closed-form formulas in terms of the solid's edge length, not eyeballed. Drag to orbit and scroll to zoom exactly as you would with a physical model on a desk, drag the cross-section slider to cut a real-time clipping plane through the solid and see its interior, and watch the numbers respond instantly as you resize it: cube volume grows with the cube of the edge, a dodecahedron's twelve pentagonal faces and thirty edges always satisfy V − E + F = 2, and the torus — the one shape in the set that is not simply connected — reports a Euler characteristic of 0 instead.