All 5 Platonic solids, interlocked. CC BY-SA, free today.
AlbertPCarpenter dropped all five Holden Platonic radial polylinks on Cults3D today under CC BY-SA — five interlocking-ring geometry sculptures from tetrahedron (4 rings, 1–2h) to icosahedron (30 rings, 6–10h). No supports, PLA, no assembly. STEM gift niche on Etsy: $5–8 per piece, $28–40 boxed set.
Five square rings, woven through each other so tightly that none can move — yet none are glued, pinned, or fastened. That's a Holden polylink. AlbertPCarpenter just dropped the complete set of five (one per Platonic solid) on Cults3D this morning, free under CC BY-SA. 1
Quick reference
| Field | Details |
|---|---|
| Model | The HOLDEN-PLATONIC RADIAL POLYLINKS (All 5) |
| Designer | AlbertPCarpenter (455 designs, ~2k downloads) |
| Platform | Cults3D |
| License | CC BY-SA — commercial use allowed with attribution |
| Files | 5 STL files (~100 mm per axis each) |
| Category | Education / geometry |
| Published | June 12, 2026 |
| Download | cults3d.com — free |
What you're printing
A Holden radial polylink is a set of square rings arranged so their edges pass through each other at precise angles matching a Platonic solid's symmetry. The result is a rigid-feeling cage that requires no fasteners — the geometry locks itself. Alan Holden described the concept in his 1983 book Orderly Tangles; this file set covers all five possible Platonic cases: 1
| Solid | Rings | STL size (mm) |
|---|---|---|
| Tetrahedron | 4 | 101.5 × 85.0 × 100.0 |
| Octahedron | 6 | 100.0 × 100.0 × 100.0 |
| Cube | 6 | 100.0 × 100.0 × 100.0 |
| Dodecahedron | 12 | 104.7 × 94.0 × 100.0 |
| Icosahedron | 30 | 106.2 × 101.5 × 100.0 |
The icosahedron is the wild one — thirty rings locked together into a sphere-like shell that looks structurally impossible until you hold it.
Print settings
The listing page carries no print settings. Based on the geometry (open ring frames, no overhangs that project inward, self-supporting structure), these inferred settings are a reasonable starting point:
| Parameter | Recommended |
|---|---|
| Layer height | 0.2 mm |
| Infill | 15–20% (rings are mostly solid walls anyway) |
| Supports | None required — the frame geometry self-supports |
| Material | PLA (stiff, easy to tune, good detail) |
| Bed adhesion | Brim recommended for the tetrahedron (wider footprint) |
| Difficulty | Intermediate — no assembly, but bridging tolerances on the interlocking edges need a well-calibrated printer |
Print each STL file as a separate print. Estimated time ranges from 1–2 hours for the tetrahedron up to 6–10 hours for the icosahedron at 0.2 mm. No post-processing beyond support removal (if you add any) — straight off the bed.
Color tip: Print each ring in a different filament color before assembly? These are already-interlocked single-piece prints, so mid-print filament swaps are your main option for multi-color. A manual swap at roughly one-third and two-thirds height gets you a tricolor ring.
Sales angle
The STEM gift niche is real and underserved on Etsy. Search "math gift teacher" or "geometry desk decor" and you'll find painted resin, laser-cut wood, and mass-produced plastic — almost nothing FDM-printed to this precision. That's the gap.
Pricing targets:
- Tetrahedron (4 rings): $5–8 — fast print, strong visual, low risk
- Full set of 5 (boxed): $28–40 — anchors the "collector" or "STEM classroom" framing
The dodecahedron and icosahedron are the showpieces; the tetrahedron and cube are the fast movers. List all five individually, bundle the full set, and offer a "teacher's classroom set" of 3× tetrahedra at a slight discount.
Who's buying: math teachers stocking their classrooms, engineering students who want something on their desk, parents shopping for a kid who "likes puzzles," and the occasional person who read Orderly Tangles in college and never forgot it.
License note: CC BY-SA allows commercial sale. You must attribute AlbertPCarpenter and release any derivative works under the same CC BY-SA license. Printing and selling the unmodified STLs is fine. 1
One real caveat: this model dropped today with zero downloads and zero makes. You'll be the first to print it for sale, which means you're also doing the settings calibration work. Budget a test print before you list.
Download: The HOLDEN-PLATONIC RADIAL POLYLINKS (All 5) on Cults3D — free, CC BY-SA.
Cover image: AlbertPCarpenter / Cults3D, CC BY-SA
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