Drag to rotate the flat diagram · pick a different outer face to reshape the same graph
This is not a rotated 3D wireframe. Every polyhedron here is a planar graph: one face is stretched into the outer boundary and the rest is solved flat with Tutte's barycentric algorithm (each inner vertex sits at the average of its neighbours) — the classic construction of a Schlegel diagram. The counts come from the same combinatorics as the 3D solid, so χ still resolves to 2.