What question did this study set out to answer?

The research aims to classify tiling configurations of the plane using two types of tiles based on their areas and to analyze their isoperimetric properties.

February 27, 2026Transactions of the American Mathematical Society

Periodic double tilings of the plane

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The research aims to classify tiling configurations of the plane using two types of tiles based on their areas and to analyze their isoperimetric properties.
Studied tilings of the plane with two repeating tiles of different assigned areas.
Classified isoperimetric configurations under fixed and arbitrary periodic lattices.
Computed the isoperimetric profile for different configurations.
Identified three distinct configurations based on the area ratio of the two tiles.
Noted variations in the number of circular edges among configurations.
Demonstrated differing optimal lattices for each configuration.

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Implication

Classifies isoperimetric configurations of periodic tilings in relation to area ratios, suggesting potential for further exploration.

Cite This Study

Nobili et al. (2026) studied this question.

synapsesocial.com/papers/69a13571ed1d949a99abf4b2 https://doi.org/10.1090/tran/9629

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Periodic double tilings of the plane

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Periodic double tilings of the plane

Key Points

Discussion

Implication

Cite This Study

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