terraform-playground/snub-dodecahedron/README.md

Foldable snub dodecahedron net

Generate a 3D-printable flat net of a snub dodecahedron that you print in one (or a few) flat pieces, then fold along beveled hinges and glue into the finished Archimedean solid.

This was inspired by the Wikipedia net Snub_dodecahedron_flat.svg. Rather than tracing that bitmap-ish SVG, the geometry here is generated from the exact coordinates of the snub dodecahedron, so every face is a perfect regular polygon and every fold angle is computed from the solid's true dihedral angles.

The flat net (one piece)	A single fold groove	Folds into this

The 92 faces (12 pentagons + 80 triangles) unfold into a single non-overlapping net with 91 fold hinges and 59 glue seams. Pentagons are shown orange, triangles blue; green fold lines are triangle–triangle edges and magenta fold lines are triangle–pentagon edges.

The actual generated 3D plate (grooves cut on the inner side):

How the folding works

The net prints as a flat plate of thickness T:

 z = T   outer surface of the finished solid  (stays continuous over folds)
 z = 0   inner surface                        (the V-grooves open here)

To fold two adjacent panels from flat (180°) to the solid's interior dihedral angle θ, a V-groove is removed from the inner side along the shared edge. When the groove closes, the panels sit at θ. A thin web of material is left at the top as a living hinge.

fold angle  = 180° − θ
each groove wall is cut at   γ = (fold + slack) / 2   from vertical
groove half-width at base    w = (T − web) · tan(γ)

The snub dodecahedron has exactly two distinct dihedral angles, so two groove sizes are produced automatically:

Edge type	Dihedral θ	Fold (180−θ)
triangle–triangle	164.175°	15.825°
triangle–pentagon	152.930°	27.070°

slack (default 6°) makes every groove slightly wider than strictly necessary. The panels can then always reach θ — in fact they can over-close by slack degrees — so any small gap at the target angle is simply filled with glue. This follows the "leave more room than necessary" bias: it is far easier to fill a gap with glue than to fight a groove that closes too early.

Glue seams (edges where two far-apart parts of the net meet only after folding) are chamfered on each mating face by the same γ, so the two faces end up coplanar and glue flush at the correct angle.

Requirements

This project is run with uv. The Python scripts carry inline dependency metadata (PEP 723), so uv run automatically creates an isolated environment with numpy/scipy on first use — there is nothing to install manually.

# install uv (see https://docs.astral.sh/uv/getting-started/installation/)
curl -LsSf https://astral.sh/uv/install.sh | sh    # or: pip install uv

# OpenSCAD is only needed to render STLs (the .scad is written regardless)
sudo apt-get install openscad                      # or https://openscad.org

Usage

# default: 30 mm edges, 3 mm thick, single net, writes out/snub_net.scad + preview
uv run generate.py

# pick your own size/depth and also render an STL
uv run generate.py --edge 35 --depth 4 --web 0.6 --slack 6 --stl

# split into smaller pieces (≤ 20 faces each) for easier printing/handling
uv run generate.py --max-faces-per-piece 20 --stl

# also export the target solid as a reference model
uv run generate.py --solid

Open the generated .scad in OpenSCAD (or use --stl) to get a mesh, then slice and print.

Parameters

Flag	Default	Meaning
--edge	30	edge length of every polygon (mm) — sets overall size
--depth / --thickness	3	plate depth / material thickness T (mm)
--web	0.6	living-hinge web left at the top of each groove (mm)
--slack	6	extra fold opening added to every groove (degrees)
--over	0.4	run grooves this far past each vertex for a clean fold (mm)
--max-faces-per-piece	—	split the net into pieces of at most N faces
--no-boundary-bevel	off	leave glue-seam edges square instead of chamfered
--solid	off	also export the reference snub dodecahedron solid
--stl	off	render an STL via the openscad CLI
--out	out/snub_net	output path prefix

Printing & assembly

1. Orientation: print the plate inner (grooved) side down on the bed. Every bevel wall is within ~γ of vertical (< ~20°), so the grooves are self-supporting — no support material needed.
2. Material: PLA/PETG work. The web is a living hinge: with a single fold it survives easily. For repeated folding or brittle filament, increase --web, or reduce it toward ~0.4 mm for an easier fold.
3. Fold each hinge until the groove walls meet (or until the faces look right). The grooves are valley folds toward the inner side.
4. Glue the 59 seams (and the hinge grooves, if you want a rigid result). The chamfered seam faces meet flush; fill any slack gap with glue.

Tip for choosing a size: the finished solid's circumradius is about 2.16 × edge, so its overall diameter is about 4.31 × edge. So 30 mm edges give a ball roughly 130 mm across.

Files

File	Purpose
snubgeom.py	exact snub dodecahedron geometry; self-verifies counts, edge lengths and dihedral angles
unfold.py	unfolds the solid into non-overlapping flat net piece(s)
scadgen.py	turns a net into beveled, grooved OpenSCAD
preview.py	SVG preview of the net + independent overlap check
generate.py	command-line driver tying it all together

Verification

Running any of the scripts re-verifies the geometry: 60 vertices, 150 edges, 92 faces (12 pentagons + 80 triangles), all edges equal length, and dihedral angles matching the known 164.175° / 152.930°. The unfolder additionally runs an independent SAT overlap check to confirm no two faces overlap in the layout.

uv run snubgeom.py     # prints the verified geometry stats
uv run preview.py      # writes net_preview.svg, reports overlapping pairs (0)