Growth functions of periodic space tessellations
2025
Growth Functions of Periodic Space Tessellations
publication
Evidence: high
Author Information
Author(s): Bartosz Naskręcki, Jakub Malinowski, Zbigniew Dauter, Mariusz Jaskolski, A. Altomare
Primary Institution: Adam Mickiewicz University, Poznań, Poland
Hypothesis
What are the growth functions for periodic tessellations of the plane by congruent polygons?
Conclusion
The study derives polynomial growth functions that count the numbers of vertices, edges, and faces in periodic tessellations as coverage expands.
Supporting Evidence
- The study provides rigorous mathematical proofs for the derived growth functions.
- Graphical representations of growth functions are created using orphic diagrams.
- Examples of 3D space groups are included to illustrate the complexity of growth functions.
Takeaway
This study looks at how shapes fit together in a flat space and counts how many corners, edges, and faces there are as you cover more area with those shapes.
Methodology
The growth functions are computed as polynomial formulas in a Python program and analyzed graphically using orphic diagrams.
Digital Object Identifier (DOI)
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