What question did this study set out to answer?

This research focuses on studying C 1-regular surfaces and their properties related to tiling with finite edge prototiles.

Tileable surfaces

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Research shows the characteristics of finite edge prototile configurations in surfaces, highlighting challenges in tiling polyhedra.

This research focuses on studying C 1-regular surfaces and their properties related to tiling with finite edge prototiles.
Constructed examples of tileable surfaces with various topologies.
Developed a framework for systematic study of monotilings.
Classified monotilings using tiles with three or fewer edges.
Identified and described all monotilings with finite edge prototiles.
Provided an example where a monohedral polyhedron cannot be smoothed to a tileable surface.
Listed open problems related to the study of tileable surfaces.

Brander et al. (2026) studied this question.

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View Full Paper

Ask AI

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Authors

Research shows the characteristics of finite edge prototile configurations in surfaces, highlighting challenges in tiling polyhedra.

This research focuses on studying C 1-regular surfaces and their properties related to tiling with finite edge prototiles.
Constructed examples of tileable surfaces with various topologies.
Developed a framework for systematic study of monotilings.
Classified monotilings using tiles with three or fewer edges.
Identified and described all monotilings with finite edge prototiles.
Provided an example where a monohedral polyhedron cannot be smoothed to a tileable surface.
Listed open problems related to the study of tileable surfaces.

Brander et al. (2026) studied this question.

View Full Paper

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Bookmark