Each of the 16 tiles keeps its position, tilt and contact-face height. Only its flat board's outline changes: four edges slide and tilt outward until a real constraint stops them. The 5 mm corner chamfers stay, because the v1 shell was solved to clear chamfered corners and the optical sensors sit in them.
An edge stops moving at the first of these. Every limit is checked in 3D, on the real tile frames.
| constraint | rule |
|---|---|
| neighbouring stacks | board stack (contact face to back parts, 5.5 mm) ≥ 1.0 mm from every neighbour's stack; ≥ 0.6 mm from its pin zone |
| cuff line | every corner, projected onto the scalp, stays above the beanie cuff line |
| shell | back parts stay inside the v1 shell's inner face less 0.5 mm, so the shell does not get thicker |
| hub | every stack ≥ 3 mm from the EXO-430 hub and its REF/BIAS pins |
| pins | a nut site gets a contact only if its pin is ≤ 13 mm raw (it rounds into the 12.5 mm EXO-5125) |
Clearances are separating-axis lower bounds on convex prisms, so the true gaps are at least these. Contacts sit on a 5.3 mm grid, rotated and offset per board to fit the most nut sites.
| tile | region | area vs square | contacts | corner angles (°) | pin raw (mm) |
|---|
A flat sheet can bend around one axis freely, but the head curves in two directions at once. Pulling a tile-sized sheet onto it means stretching the sheet in its own plane, and copper on polyimide is made to bend, not stretch. The layout already measures this for every tile: 1.4–2.0 % of in-plane strain for a 44 mm sheet. That is far past what copper traces survive, so a whole-tile flex board would wrinkle or crack.
| option | coverage | contacts sit | designs | main problem | verdict |
|---|---|---|---|---|---|
| Rigid squares (today) | 63.5 % | flat board, pins 7.5–12.5 mm | 1 | corners sit 6.4 mm farther from the scalp than the centre, so the helmet is about 12 mm thicker | bench order |
| Rigid irregular quads (this page) | 86 % | same | 16 contact boards, maybe 16 controllers | 16 routes and 16 PCBA setups per order | possible |
| One flex sheet per tile | high | on the curve | 1 | needs 1.4–2 % stretch; and the board needs 6 layers with HDI vias, which is specialist flex work | no |
| Slit / petal flex (kirigami) | high | on the curve | 1 | every pin needs a nut, a follower within 2 mm and a stiffener, which leaves little bendable flex; the converters and their 0.4 mm pins still need a rigid, multilayer spot | hard |
| Rigid-flex islands | ≈ as quads or better | near the curve | 1 | rigid-flex fabrication and folded assembly cost more; the islands still need fine-pitch multilayer routing | best v2 candidate |
Recommendation: keep the routed square boards for the 1–2 tile bench order. Take irregular quads only if the gain is wanted before a redesign. Treat rigid-flex islands as the v2 study, and get a rigid-flex quote and a one-island prototype before changing the architecture.
Inputs: out/layout.json (tile frames), out/pcb/tile_geom.json (contact-face heights, pin table), out/shell_v1_report.json (shell inner face 23.2 mm). Output: out/quad_layout.json. Generated 2026-10-27.