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Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
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Geometrically Interlocking Space-Filling Tiling Based on Fabric Weaves.

Vinayak R Krishnamurthy, Ergun Akleman, Sai Ganesh Subramanian

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    This study presents woven tiles, a novel space-filling shape system designed using Voronoi partitioning and fabric weave patterns. These interlocking tiles offer a new approach to geometric design and fabrication.

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    Area of Science:

    • Computational geometry
    • Materials science
    • Geometric design

    Background:

    • Traditional space-filling shapes often lack inherent interlocking properties.
    • Fabric weaving patterns offer complex geometries with inherent symmetry and interlocking potential.

    Purpose of the Study:

    • To introduce a general framework for designing and fabricating geometrically interlocking, space-filling shapes called woven tiles.
    • To demonstrate the application of this framework using fabric weave patterns on flat and curved surfaces.
    • To analyze the mechanical behavior of the fabricated woven tiles.

    Main Methods:

    • Utilizing Voronoi partitioning with curve segments as sites.
    • Designing curve segments based on symmetry-closed weave patterns (plain, twill, satin).
    • Fabricating woven tiles on flat and curved domains.
    • Evaluating mechanical properties via finite element analysis.

    Main Results:

    • Successful design and fabrication of woven tiles based on common 2-fold fabric weaves.
    • Demonstrated interlocking and space-filling capabilities of the woven tiles.
    • Comparative analysis of the mechanical behavior of tiles fabricated from different weave patterns.

    Conclusions:

    • The proposed framework enables the creation of novel, interlocking, space-filling geometric shapes.
    • Woven tiles offer a versatile design approach applicable to various surfaces.
    • Finite element analysis provides insights into the mechanical performance of these unique structures.