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bikar · pattern decomposition · the fork

Three ways to pin a pattern

You want Adjacent-10 broken into pieces that each carry pins on the LEGO grid. There are three honest ways to do that, and they don't agree. Each panel runs its rule on the real 31-face pattern — 20 triangles, 10 kites, one central decagon — live, so you see what actually lands where before we build anything.

The pattern, unaltered. A 10-fold rosette: kites in amber, triangles and the decagon in slate — bikar's Adjacent-10. None of its faces are grid rectangles — that one fact is what splits the three options apart. And how big you print it changes everything — drag the size below and watch Option 2 anchor.

Option 3 · ships today

Rectangular grid

The current mural. Cut on the 8 mm grid into rectangles; art rides on top as relief.

Option 1 · new engine work

Shape-faithful · grid pins

One piece per face. Pins drop at the stud crossings inside each face — still snaps to a baseplate, but the count rides on printed size.

Option 2 · leaning here

Shape-faithful · centre pins

One piece per face, one pin at its deepest point, into a board we co-print. Drag size up until every face turns solid — that's all anchored.

pin (⌀3.2 mm) tube (grid crossing) 3.1 mm clearance it needs face too small to seat a pin 8 mm stud grid

The pick

Option 2 — shape-faithful pieces, one pin at each face's deepest point, into a board we co-print. A 10-fold pattern's face centres involve decagonal (golden-ratio) coordinates that never all land on a square 8 mm lattice, at any scale — so the holes have to be drilled to match the pins, which means we generate the board from the same cut. The pin's only job is to resist lift-off; sideways shift and rotation are held by the pieces butting edge-to-edge in the tiling, so one centre pin per piece is enough.

The size threshold is a validator, not a guess

Drag the size: below ~100 mm the small filler triangles can't seat a ⌀3.2 mm pin and go red; at the computed threshold all 31 anchor. That number is derived live from the real geometry — the smallest width at which every face's deepest interior point clears the 1.6 + 1.5 mm a pin needs — so a V-seat validator can assert it rather than a person eyeballing it.