@@ -85,6 +85,7 @@
     "examples/shader-node-group",
     "examples/shape-key-blend",
     "examples/sky-texture-sun-elevation",
+    "examples/soccer-ball-goldberg",
     "examples/swatch-grid",
     "examples/temp-override-join",
     "examples/text-version-stamp",
 
@@ -516,3 +516,16 @@ jobs:
           # on failure.
           xvfb-run -a "$BLENDER" --background \
             --python examples/prop-origin-transform/prop_origin_transform.py --
+
+      - name: Shipped example - soccer ball Goldberg (polyhedron invariants + panel binding)
+        run: |
+          set -euo pipefail
+          # Check only (no render): a bmesh icosphere truncated at 1/3 per edge
+          # into the Goldberg polyhedron; asserts closed-form counts (60/90/32,
+          # Euler 2), 12-pentagon/20-hexagon census, uniform degree 3,
+          # watertightness, edge-length uniformity, face planarity vs an
+          # independent Newell normal, centroid-at-origin circumsphere, and
+          # panel materials bound by face vertex count. Exits non-zero on
+          # failure.
+          xvfb-run -a "$BLENDER" --background \
+            --python examples/soccer-ball-goldberg/soccer_ball_goldberg.py --
@@ -18,7 +18,7 @@
 </p>
 
 <p align="center">
-  <strong>12 skills</strong> &nbsp;&bull;&nbsp; <strong>6 rules</strong> &nbsp;&bull;&nbsp; <strong>2 templates</strong> &nbsp;&bull;&nbsp; <strong>17 snippets</strong> &nbsp;&bull;&nbsp; <strong>36 examples</strong>
+  <strong>12 skills</strong> &nbsp;&bull;&nbsp; <strong>6 rules</strong> &nbsp;&bull;&nbsp; <strong>2 templates</strong> &nbsp;&bull;&nbsp; <strong>17 snippets</strong> &nbsp;&bull;&nbsp; <strong>37 examples</strong>
 </p>
 
 <p align="center">
@@ -36,7 +36,7 @@
 
 ## Overview
 
-This repository ships **12 skills, 6 rules, 2 templates, 17 snippets, and 36 runnable examples** for Blender Python development targeting Blender 5.1 (current stable) with Blender 4.5 LTS fallback support.
+This repository ships **12 skills, 6 rules, 2 templates, 17 snippets, and 37 runnable examples** for Blender Python development targeting Blender 5.1 (current stable) with Blender 4.5 LTS fallback support.
 
 The content is consumed by AI coding agents (Cursor, Claude Code, any MCP-capable client) when working on Blender add-ons, geometry nodes scripts, batch pipelines, or animation tooling. There is no build step. Edit the markdown and Python files directly.
 
@@ -700,6 +700,26 @@ Extends [`parent-inverse-orrery`](examples/parent-inverse-orrery/) without
 retreading orbits. Dual-panel still: TRAP (bare parent — empty socket +
 teleported flange) vs MPI KEEP.
 
+</td>
+</tr>
+<tr>
+<td width="46%" valign="middle">
+<a href="examples/soccer-ball-goldberg/"><img src="examples/soccer-ball-goldberg/preview.webp" alt="Soccer ball Goldberg: a white soccer ball with black pentagon panels on a dark studio floor — a bmesh icosphere truncated at one-third per edge into the Goldberg polyhedron, proving closed-form counts, uniform degree, equal edges, planar faces, one circumsphere, and panels bound by face vertex count" /></a>
+</td>
+<td valign="middle">
+
+### [soccer-ball-goldberg](examples/soccer-ball-goldberg/)
+
+The truncated icosahedron as a bmesh contract: every icosphere edge cut at
+exactly `1/3`, faces ordered by link-topology walks (nothing hand-listed),
+and every invariant asserted as a closed form — `60/90/32`, Euler 2, uniform
+degree 3, edge lengths within 3e-5, planar faces against an independent
+Newell normal, one circumsphere, and the black pentagons / white hexagons
+bound by face vertex count, never enumeration order. Sibling to
+[`bmesh-gear`](examples/bmesh-gear/) (parametric extrusion): this one
+witnesses polyhedral invariants plus per-face-class material binding. The
+smoothed render inverts on sight if the panel binding does.
+
 </td>
 </tr>
 </table>
 
@@ -120,6 +120,11 @@ Not committed; target list for the next content version. (v0.3.0 shipped the smo
 - Volumetric scatter optical-depth witness: Volume Scatter density → Beer–Lambert transmittance along a known path (Cycles; Stage deviation)
 - Freestyle SVG / line-set witness: Freestyle line set on a silhouette (full render pass; prefer Line Art first)
 - ~~prop-origin-transform witness~~ **SHIPPED** as `examples/prop-origin-transform/` — origin to base center + data-API scale apply + `matrix_parent_inverse` for a bolted accessory; scale `(1,1,1)`, local `min.z==0`, world AABB delta 0, bare jump ~0.43 m, MPI err ~3e-8; stale `matrix_world` until `view_layer.update()`; byte-identical on 4.5.11 and 5.1.2
+- ~~Goldberg polyhedron topology witness~~ **SHIPPED** as `examples/soccer-ball-goldberg/` — soccer ball as a truncated icosahedron: bmesh icosphere cut at 1/3 per edge, faces ordered by link-topology walks; closed forms 60/90/32 + Euler 2, census 12×5+20×6, uniform degree 3, edge dev 6.5e-06, planarity 1.9e-06 (independent Newell normal), circumsphere dev 9.0e-06, panels bound by face vertex count (enumeration-order probes exit 13); float32 noise floor ~9e-6 → 3e-5 gates; byte-identical on 4.5.11 and 5.1.2
+- Mirror-modifier symmetry witness: half-model completed by Mirror evaluated through the depsgraph — evaluated-vs-original counts (2n − welded centerline), exact ±X partner for every evaluated vertex, merge-threshold weld proof, failure dramatically visible (half a subject / split seam). Strongest subject: a generic vehicle body
+- Chess-piece lathe witness: a turned piece (rook/pawn) via Screw modifier or bmesh spin from an authored profile — evaluated verts == profile × steps (minus pole merges), ring radii match the profile closed form, axis of revolution exact
+- Dice-pair per-face witness: material/attribute assignment driven by face normal direction, opposite-faces-sum-to-7 as an independently computed invariant, pip placement from a closed-form lattice
+- Bicycle-wheel radial witness: spokes via radial Array with object offset — exact angular spacing, spoke count, hub/rim concentricity, every evaluated spoke endpoint on its computed rim coordinate
 - ~~mesh-hygiene-audit witness~~ **SHIPPED** as `examples/mesh-hygiene-audit/` — engine-ingest topology checklist on a stepped street electrical pedestal: no ngons, no loose verts, manifold edges (exactly 2 faces), no zero-area faces (`min_area` printed), positive signed volume, Euler `V−E+F==2` (24/44/22, volume 0.989248); byte-identical on 4.5.11 and 5.1.2; dual-panel dirty vs clean still
 - UV atlas pack witness — lightmap/unique UV island packing with non-overlap + utilization closed forms (deferred behind hygiene/origin; overlaps `uv-layer-grid` / `triangulate-tangents` / `gltf-export-roundtrip` UV arc)
 - Attribute domain witness: writing a POINT-domain color attribute and reading it as if it were CORNER (or vice versa) silently shears colors across shared verts — companion to `color-attribute-wheel`
 
@@ -609,6 +609,17 @@ <h2><a href="prop-origin-transform/">prop-origin-transform</a></h2>
           <a class="card-link" href="prop-origin-transform/">View example <span aria-hidden="true">&rarr;</span></a>
         </div>
       </article>
+      <article class="card" data-tags="bmesh mesh">
+        <a class="card-media" href="soccer-ball-goldberg/" aria-label="soccer-ball-goldberg example detail page">
+          <img src="assets/soccer-ball-goldberg-hero.webp" alt="soccer-ball-goldberg — A soccer ball as a Goldberg polyhedron: a bmesh icosphere truncated at 1/3 per edge, faces ordered by link-topology walks, panels bound by face vertex count." loading="lazy" decoding="async" />
+        </a>
+        <div class="card-body">
+          <h2><a href="soccer-ball-goldberg/">soccer-ball-goldberg</a></h2>
+          <p class="teaches">A soccer ball as a Goldberg polyhedron: a bmesh icosphere truncated at 1/3 per edge, faces ordered by link-topology walks, panels bound by face vertex count.</p>
+          <p class="witnesses"><span class="tag">witnesses</span> Goldberg invariants are closed forms — counts, degree 3, uniform edges, planar faces, one circumsphere — and panels bind by vertex count, never enumeration order.</p>
+          <a class="card-link" href="soccer-ball-goldberg/">View example <span aria-hidden="true">&rarr;</span></a>
+        </div>
+      </article>
     </div>
   </main>
   <footer>
 
@@ -190,7 +190,7 @@ <h1>prop-origin-transform</h1>
 <ul><li><strong>Stale <code>matrix_world</code>.</strong> After a location edit, <code>matrix_world</code> is unchanged until <code>view_layer.update()</code> (same half of the orrery contract).</li><li><strong>Scale apply via data API.</strong> Non-uniform scale baked into verts; <code>obj.scale == (1,1,1)</code> exactly afterward.</li><li><strong>Origin at base center.</strong> Local bbox <code>min.z == 0</code>, XY centered; world AABB delta across the bake is <strong>0</strong> (gate <code>1e-5</code>).</li><li><strong>Bare-parent trap.</strong> Parenting the accessory without MPI jumps it (~0.43 m measured); setting <code>matrix_parent_inverse</code> restores world location (err ~3e-8).</li></ul>
 <p><strong>What each check catches on failure:</strong> skipping scale apply leaves non-identity scale; skipping origin bake leaves <code>min.z ≈ -0.756</code>; skipping MPI leaves the accessory teleported.</p>
 <p><strong>Version witness:</strong> byte-identical numbers on Blender 4.5.11 LTS and 5.1.2.</p>
-<p>The render is a dual panel: left <strong>TRAP</strong> (bare parent — accessory teleports, hazard material) vs right <strong>MPI KEEP</strong> (accessory stays put), with emissive origin markers at each pedestal&#x27;s base.</p>
+<p>The render is a dual panel: left <strong>TRAP</strong> (bare parent — flanged conduit teleports off an empty mount socket, hazard material) vs right <strong>MPI KEEP</strong> (flange seated in the socket), with emissive origin markers at each pedestal&#x27;s base. Check closed forms are unchanged; the flange/socket are render form only.</p>
 <h2>Run</h2>
 <pre><code>blender --background --python prop_origin_transform.py --
 blender --background --python prop_origin_transform.py -- --output origin.png