3Dtilasta
3Dtilasta is a theoretical framework for constructing and analyzing tilings of three-dimensional space using a finite set of polyhedral tiles. It generalizes two-dimensional tiling concepts to the volumetric domain by enforcing local compatibility conditions on tile facets to achieve gap-free assemblies. The framework emphasizes regularity and scalability, supporting both periodic arrangements and certain classes of aperiodic tilings suitable for complex volumetric structures.
Tiles in 3Dtilasta are polyhedra with labeled faces and oriented edges. Adjacent tiles must match face labels
Algorithmically, 3Dtilasta uses constructive rules, local replacement schemes, and search-based generation to produce tilings. It also
Applications include architecture and digital fabrication, where repeatable 3D tilings can guide modular construction, as well
In scholarly contexts, 3Dtilasta is discussed alongside classical tiling theory, convex polyhedra, and lattice-based methods. While