• Models
  • Contests
  • Slicer
  • Login
  • Start Here
    thingiverse-iconprintables-iconcults3d-iconmakerworld-iconmyminifactory-icon

    3D GO

    3D ModelsContestsCollectionsSaved ModelsOn a mobile device?

3D GO

Privacy Policy
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Image 1
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Image 2
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Image 3
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Image 4
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Image 5
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Thumbnail 1
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Thumbnail 2
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Thumbnail 3
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Thumbnail 4
Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi] 3D Printer File Thumbnail 5

Aperiodic Monotile polykite "The Hat" Einstein - [multiple aspect ratios include Phi]

DockGuy avatarDockGuy

March 30, 2023

printables-icon
DescriptionCommentsTags

Description

This is a little different than other monotile uploads here. I've taken the extra step to produce multiple aspect ratios for the right-angle edges. So you can have a different monotile set than everybody else ;)

My favorite is the Phi ratio.

 

At some point I'll upload an OpenSCAD model that is configurable for an infinite number of ratios…

 

 

The gray “hat” polykite tile is an “einstein”, an aperiodic monotile. In other words, copies of this tile may be assembled into tilings of the plane (the tile “admits” tilings), yet copies of the tile cannot form periodic tilings, tilings that have translational symmetry. In fact, the tile admits uncountably many tilings. Credit: arXiv (2023). DOI: 10.48550/arxiv.2303.10798

  • https://arxiv.org/pdf/2303.10798.pdf
  • https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/

 

 

License:

Creative Commons — Attribution

Related Models

#3DBenchy - The jolly 3D printing torture-test by CreativeTools.se preview image

#3DBenchy - The jolly 3D printing torture-test by CreativeTools.se

CreativeTools profile image

CreativeTools

90,896

Flying Night Dragon preview image

Flying Night Dragon

Sevro profile image

Sevro

8,740

Checklist personnalisable pour enfants preview image

Checklist personnalisable pour enfants

Mik3Dprint profile image

Mik3Dprint

1,252

The T-Rex Skull preview image

The T-Rex Skull

MakerBot profile image

MakerBot

39,822

Stable Flyer VI - Small Toy Glider preview image

Stable Flyer VI - Small Toy Glider

João Hackbart profile image

João Hackbart

3,743

ALPHABET PUZZLE - Montessori Letter Puzzle preview image

ALPHABET PUZZLE - Montessori Letter Puzzle

3DPTK.com profile image

3DPTK.com

747

Plantygon - Modular Geometric Stacking Planter for Succulents preview image

Plantygon - Modular Geometric Stacking Planter for Succulents

Printfutura profile image

Printfutura

28,535

Upcycled ATX Lab Bench Power Supply preview image

Upcycled ATX Lab Bench Power Supply

Caelestis Workshop profile image

Caelestis Workshop

1,513