Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.11281 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- We study $C^1$-regular surfaces in $R^3$ that admit tilings by a finite number of rigid motion congruence classes of tiles. We construct examples with various topologies and present a framework for a systematic study, mainly concentrating on monotilings. A finite edge prototile is a tile that has only a finite number of possible interfaces with adjacent copies of itself. We describe all monotilings by such tiles with three or less edges. We consider the question of whether a monohedral polyhedron can be smoothed to become a finite edge type tileable surface with the same graph structure, and we give an example where this is not possible. Finally we list some open problems.