# HEX-CELL — the fundamental LightCell tower unit (operator design, 2026-07-16)

Provenance: Danielle's notebook sketch + terminal dictation, 2026-07-15/16 session.
Status: geometry verified arithmetic; costs are retail-anchored estimates; chemistry flags open.

## The unit

Form 4 (SLA) printable alumina hexagonal tile, sized to the printer envelope:

| Parameter | Value | Note |
|---|---|---|
| Hex side a | 87 mm | flat-to-flat = a·√3 ≈ **150.7 mm** = Form 4 print envelope; the print IS the tile (shrinkage factored, curable in-house ovens) |
| Hex footprint | 0.0197 m² | (3√3/2)a² |
| Inscribed circle | 150 mm ⌀ | 101.6 mm (4") quartz tube seats inside with ~24 mm annular margin |
| Quartz tube | 101.6 mm ⌀ × 1257 mm (4" × 49.5") | patio-heater commodity, $49.62 retail ea (Amazon, purchased) |
| Tube L/D | 12.4 | good cavity aspect; per-end loss solid angle ~1/(4·L/D²), sub-% |
| Emitter side area per cell | π·0.1016·1.257 ≈ **0.40 m²** | vs 0.02 m² footprint → **20× area gain vertical** — the tower thesis in one ratio |
| Cell pitch height | ~1333 mm target | 76 mm header/injector/plenum per cell |
| Emitter bore | ≤50 mm radius, likely smaller | quartz outer + sprung PCA inner option |

## Functions of the tile (one part, five jobs)
1. **Seat + salt bed**: tube sits on a salt/salted surface. The salt seat IS the Na cold-spot
   reservoir — seat temperature (forced-air on the cold end) pins P_Na → vapor density.
   Transport design knob physically located (see feedback_no_fabricated_limit_thresholds.md:
   condensation = transport, not a limit).
2. **White cavity**: alumina diffuse reflectance ~0.9+ visible; missed photons recycle.
   Shared hex walls = shared Lambertian cavity surfaces; honeycomb = structure + manifold + integrating cavity.
3. **Universal coaxial holder**: one printed bore accepts vacuum jacket / smaller quartz /
   PCA tube / ITO hot-mirror sleeve / air gap. **Tile = ISA; emitters = implementations.**
   Emitter R&D iterates inside a frozen mechanical interface.
4. **Low-temp injector/nozzle block**: printed alumina lives only at the cool ends;
   honeycomb extrusion runs top-to-bottom; peak flux never touches the printed part.
5. **Stackable**: cells stack vertically; forced air on the cool end, axial gradient by geometry.

## Cost stack (retail-anchored, direction not precision)
- Quartz tube: $49.62 retail → est $15–25 volume (patio-heater supply chain, already commodity)
- Printed alumina: target **<10% of cell BOM** (2 hex headers per cell); already 4× below retail per operator's supplier data; drive lower
- Extruded alumina honeycomb: catalyst-substrate industry pricing — cheapest ceramic form factor extant
- Salt, springs, misc: small
- Order **$100–200/cell** before emitter internals + silicon
- Strategic frame: every major component is already down someone else's learning curve
  (quartz = patio heaters, honeycomb = catalytic converters, silicon = Swanson $0.10/W, $1.9/kg module 2024)

## Tower composition (notebook numbers)
- 42 m ⌀ → 1385 m² cross-section; ~70k cells/layer solid-packed; real design annular shell, ~27% fill note
- 420 m / 1.333 m pitch = 315 cells per column height
- Single-cell emitter area 0.4 m² → km²-class radiating surface at tower scale

## Open flags (honest)
- **Quartz vs Na at temperature**: devitrification + alkali attack on silica is the known killer.
  Cheap quartz = OUTER envelope at moderated T only; PCA/alumina inner carries the chemistry.
  This is precisely what the coaxial-holder architecture buys.
- Salt chemistry/composition for the seat unspecified.
- Sprung PCA inner: mechanical detail TBD.
- All costs retail-anchored; no supplier quotes at volume yet except operator's alumina 4×-below-retail datum.

## Sim hook
Builder game (dyson-cylinder v2c): build unit = this literal tile. Kernel R₂/L map to the cell
bore/length; cost ledger from this file; power = integrated computed spectrum × PV response.
True and epic converge at the cell, not the tower.