Platonic Solids Duality (2D)

This 2D companion flattens each Platonic solid into a Schlegel diagram — a planar graph of its vertices and edges with one face opened out as the outer boundary — and derives its dual graph live from the shared face list: a new node at every face's center, joined whenever two faces shared an edge. Switch between the tetrahedron (self-dual), the cube/octahedron pair and the dodecahedron/icosahedron pair, toggle the dual overlay, and watch the vertex and face counts swap exactly between a solid and its dual while the edge count stays fixed — the defining signature of geometric duality.