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The complete corpus of 440 verified polyhedra spanning classical regular solids, semi-regular Archimedean polyhedra, Catalan duals, uniform prisms and antiprisms, convex Johnson solids, and the exhaustive combinatorial set of small convex polyhedra (4 to 8 faces).
Mathematical synthesis, canonical midsphere realization, FDM orientation optimization, and additive manufacturing craft.
Every polyhedron in this gallery is generated from rigorous first principles, spanning classical geometry and combinatorial topology:
Home 3D printing (FDM) builds parts layer-by-layer from the bottom plate upward. If a polyhedron is printed balanced on a sharp tip (vertex) or thin edge, it will tip over, detach from the bed, or require massive disposable support scaffolding.
Stability Score(fi) = Area(fi) / Height(fi)
Our export engine evaluates every polygonal face of the polyhedron:
| Format | Role & Recommendation | Key Advantage |
|---|---|---|
| Wavefront OBJ (.obj) | Default & Recommended | Preserves true polygon boundaries ($k$-gons like pentagons and hexagons) without chopping them into triangular soup. Opens cleanly in Blender, Maya, Rhino, Fusion 360, Godot, and Unity. |
| Object File Format (.off) | Academic Standard | Universal format used in computational geometry research, CGAL, and Princeton 3D shape benchmarks. |
| Core 3MF (.3mf) | Modern Production 3D Printing | XML-based package with explicit millimeter scale units and manifold topology, native in Bambu Studio and PrusaSlicer. |
| Binary STL (.stl) | Legacy Mesh (Last Option) | Chops every face into disconnected triangles. Retained for older slicing software; placed last because it loses polygon topology. |
| Vector SVG (.svg) | 2D Graphic Design & Icons | Axonometric isometric projection rendered with CIELAB color grading, zero anti-aliasing seams, and crisp 512×512 vector lines. |
Polyhedra consist exclusively of razor-sharp dihedral edges, discrete singular vertices, and mirror-flat planar facets. Follow these slicing rules to prevent defects:
| Slicing Parameter | Recommended Setting | Engineering Rationale |
|---|---|---|
| Layer Height | 0.12 mm (or 0.16mm Adaptive) | Reduces stair-stepping ridges on shallow-sloped facets below visual detection. |
| Perimeter Walls | 4 walls (1.8 mm solid shell) | Decouples internal infill tension from exterior flat facets, eliminating visible infill "ghosting". |
| Infill Pattern & Density | 12% – 15% Gyroid | Isotropic minimal surface; prevents nozzle scraping, maintains uniform thermal shrinkage, and keeps physical center of gravity at the centroid. |
| Top Surface Pattern | Monotonic / Monotonic Line | Sweeps all parallel extrusion lines in a single direction, ensuring uniform specular sheen across flat faces. |
| Z-Seam Alignment | Sharpest Corner (Scarf Joint ON) | Hides extrusion starts and stops inside natural dihedral crease edges; prevents ugly surface "zits" on flat facets. |
| Elephant's Foot Comp. | -0.18 mm initial layer expansion | Eliminates first-layer squish bulge along the bottom perimeter edges. |
| Build Plate & Material | Smooth PEI Sheet + Matte PLA | Smooth PEI keeps the bottom face mirror-flat; Matte PLA provides diffuse light diffusion and hides micro layer steps. |
| SLA Resin Notice | Never print flat; Tilt 20°–30° | Elevate 5mm on supports anchored strictly to dihedral crease edges and bottom vertices to prevent FEP suction delamination and light-bleed bloat. |