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  • hat

  • turtle

  • Einstein

  • tiling

  • monotile

  • aperiodic monotile

The aperiodic monotile / "einstein" / "hat" from David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss (see: https://arxiv.org/abs/2303.10798), but in a variety of formats. With the included OpenSCAD file you can build it with or without a lip. (By the photos, you can see I obviously prefer it "with".)

The kites can be combined to double-kites, which can be assembled into hats. While proving the aperiodicity of the hat, the turtle and a variety of similarly aperiodic shapes were discovered.

My congrats to Smith, et al. I'm not a tiling enthusiast, nor a mathematician, but I think it's a thing of beauty.

Originality of the Model

The author declares that this work is their personally shared model

Original creator:
longbored

This model is licensed under the following terms:

Credit must be given to the creator

Models(28)

  • hat_from_single_kites-inverse.stl

    10.82 KB

    2025-06-30

  • hat_from_points-regular.stl

    4.96 KB

    2025-06-30

  • double_kite.stl

    1.84 KB

    2025-06-30

  • hat_from_double_kites-regular.stl

    6.92 KB

    2025-06-30

  • hat_from_double_kites-inverse.stl

    6.92 KB

    2025-06-30

  • hat_from_points-inverse.stl

    4.96 KB

    2025-06-30

  • hat_from_points_no_lip-inverse.stl

    2.43 KB

    2025-06-30

  • hat_from_points_no_lip-regular.stl

    2.43 KB

    2025-06-30

  • hat_from_single_kites-regular.stl

    10.82 KB

    2025-06-30

  • Aperiodic_Monotile_Builder.scad

    7.48 KB

    2025-06-30

  • hexagon.stl

    2.43 KB

    2025-06-30

  • turtle_from_points_no_lip-inverse.stl

    2.43 KB

    2025-06-30

  • turtle_from_points_no_lip-regular.stl

    2.43 KB

    2025-06-30

  • tracer_7.stl

    2.43 KB

    2025-06-30

  • quadruple_hat_from_hats-regular.stl

    20.59 KB

    2025-06-30

  • turtle_from_double_kites-regular.stl

    8.48 KB

    2025-06-30

  • turtle_from_points-inverse.stl

    4.96 KB

    2025-06-30

  • turtle_from_single_kites-inverse.stl

    13.36 KB

    2025-06-30

  • hat_special_inset-inverse.stl

    6.14 KB

    2025-06-30

  • quadruple_hat_from_hats-inverse.stl

    20.59 KB

    2025-06-30

  • tracer_6.stl

    2.43 KB

    2025-06-30

  • hat_special_inset-regular.stl

    6.14 KB

    2025-06-30

  • turtle_from_double_kites-inverse.stl

    8.48 KB

    2025-06-30

  • turtle_from_points-regular.stl

    4.96 KB

    2025-06-30

  • kite.stl

    1.45 KB

    2025-06-30

  • turtle_special_inset-inverse.stl

    8.48 KB

    2025-06-30

  • turtle_from_single_kites-regular.stl

    13.36 KB

    2025-06-30

  • turtle_special_inset-regular.stl

    8.48 KB

    2025-06-30

  • View all(28)

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