Untiling
Main Page

Research · Wiki · Materials and fabrication

Materials and fabrication

From relief panels to STL toolpaths, one patch, many physical outputs.

Cutting, molding, and toolpaths

A single generated patch exports as SVG for cutting, STL for printing, GLB for instancing, and CSV/JSON for custom toolpaths. One design becomes a relief panel, a printed texture, an instanced mesh, or a dataset of tile transforms, with identical geometry in each.[2][10]

Brass relief panel of aperiodic monotile tiles suitable for fabrication reference
Physical output reference. The same patch exports to STL or GLB for molds, relief panels, CNC toolpaths, and printed textures.

The chirality result can simplify part inventory: Spectre tilings do not require a second mirrored outline.[2] Tool count still depends on edge variants, draft, finish, and process. Community fabrication files, OpenSCAD models, STLs with orientation grids, laser-cut outlines, are indexed in the bibliography and Resources and tools. Digital monotile geometry has been used to manufacture PLA Hat-wall honeycombs[42] and PolyJet multiphase fracture panels.[46][49] Their measured performance came from the complete specimen, topology, materials, interfaces, dimensions, process, and loading, not from the export format. Monotile kirigami currently establishes deployable geometry theoretically and computationally; force, fatigue, thickness, and fabrication-tolerance tests remain open.[51]

Choosing and preparing an export

  • SVG/DXF: planar outlines for laser, waterjet, router, plotter, or print. Confirm units, closed paths, winding, duplicate edges, and whether shared edges should be cut once.
  • STL: watertight triangulated solids for printing. STL carries no reliable units, materials, hierarchy, or instance semantics, so include a manifest.
  • GLB: compact meshes, materials, and scene transforms for review or instancing. Check axis convention, transform baking, normals, and material licensing.
  • CSV/JSON: tile IDs, labels, parent clusters, positions, rotations, scale, and source version for CAM, robotics, or custom scripts. Publish a schema and coordinate convention.

Tolerance, kerf, grout, and chirality

Kerf is material removed by a cutting beam or tool. Offset toolpaths by the measured kerf, not the nominal machine setting, and cut a multi-tile coupon before a full sheet. For molded or printed parts, include shrinkage, clearance, corner radii, minimum wall thickness, and surface finish. For architectural tile, design the grout gap into the placement geometry; independently offsetting every complex outline can change which corners meet.

Preserve handedness through export and nesting. Straight Tile(1,1) and edge-modified Spectres have different reflection rules,[2] while face decoration or draft angle may make even a geometrically flippable part one-sided. Add an orientation mark and reject accidental mirror transforms in validation.

Validation workflow

  1. Hash or version the source outline and record units, scale, patch seed/root, and generator revision.
  2. Check closed polygons, self-intersection, overlap, gaps, duplicate paths, and transform handedness.
  3. Simulate nesting and tool reach; manufacture a coupon containing representative joints and corners.
  4. Measure actual dimensions, fit, warpage, and surface quality; update compensation from measurements.
  5. Dry-assemble a numbered cluster, then archive the final files, manifest, machine settings, and inspection results.

Evidence and candidate directions

  • Measured in specific specimens: printed Hat honeycombs and multiphase composite panels, including an interdigitated derivative interface.[42][46][49]
  • Constructed mathematically or computationally: topologically interlocking Spectre-derived blocks[50] and deployable monotile kirigami.[51] These papers establish geometric or kinematic possibility, not structural load capacity.
  • Paper prototyping: fold-and-cut templates produce Hat, Turtle, and straight Tile(1,1) outlines after flat folding and one cut.[67]
  • Candidate experiment: compare aperiodic and periodic infill at matched mass, process parameters, and boundary conditions; do not assume resonance or strength gains in advance.
  • Support-free printing studies, topology optimization, and surface finishing
  • Architectural panels, molds, product surfaces, screens, and repeat-free decoration
  • Physical prototyping and load testing of mathematically constructed three-dimensional topological-interlocking blocks[50]

Origami-adjacent folding studies and flat-foldable synthesis environments show how computational tools explore fold-pattern spaces[26]; monotile kirigami extends this to deployable aperiodic sheets.[51] Mechanical performance belongs to the complete specimen, material, strut thickness, joints, defects, boundaries, and loading, not to the outline alone. “Monotile-inspired” lattices should be labeled as such when they modify the canonical geometry.

See also

Design, art, and architecture, Materials science and fluids

Categories: Applications