A chapter from GIGI Builds that didn’t fit in print — playable in your browser.
Picture a cube of clay sliced into 384 identical little pyramids — that’s Kuhn’s slicing. Now imagine a sphere hidden inside the cube. Wherever a pyramid touches the sphere, we cut its longest edge in half and repeat — like a mapmaker adding detail only where the coastline is jagged. The tetrahedra hugging the sphere get tiny; the ones out in the corners stay big and lazy.
Each tetrahedron is colored by its shape family — the pattern its six inside-angles make, once you stop caring which corner you labeled first. Two tets pointing different directions but sharing the same angles belong to the same family.
That’s the “audit” part. Every tetrahedron carries its shape data with it — family, quality, sliver margin — so when you ask the mesh “is anything bad in here?” it answers on the spot. No separate analysis pass, no offline check.
Bonus chapter · GIGI Builds
The whole tetmesh above lives in GIGI as data. Every tetrahedron
becomes one record — 5,760 in total, one per tet across all four
refinement levels. Each record carries eight fields: id,
level, shape_family, obtuse_class,
q_vol (0 = flat sliver, 1 = perfectly regular),
d_bad (sliver margin), and the smallest + largest of its six
inside-angles.
Because GIGI is a fiber-bundle database, the bundle’s curvature (κ) and confidence ride along with every read — no sidecar service to compute them. When you scrub a level or hover a tet, the log below shows the real GQL query GIGI answered.
Flat line = quality holds through all four cuts. Maubach’s rule promises the blue line can’t drop below the yellow one; if it ever did, the theorem broke.