The aperiodic monotile in a variety of formats

This repository contains code and vector image files to produce the aperiodic monotiles found by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss.

There's a family of related shapes, each made of 14 edges (though two of the edges are parallel and adjacent so look like a single long edge). Each edge is one of two lengths, 𝑎 or 𝑏. The angles in the shape don't change. There is an interactive tool to draw the tiles with any choice of the parameters and download in SVG or PNG format.

There are three interesting monotiles, which each tile the plane aperiodically.

A 'hat':

A 'turtle':

And a 'spectre':

Each file produces a single copy of the tile. Several copies of the tile fit together to tile the plane:

• The 'hat' monotile can tile the plane together with its reflection.
• The 'turtle' monotile can also tile the plane with its reflection. (It and the hat are two of a family of polygons that tile the plane in the same way.)
• The 'spectre' monotile, with curved edges, can tile the plane only without its reflection. (The spectre with straight edges is related to both the hat and turtle, but it can tile the plane periodically and aperiodically. An aperiodic tiling can be forced by forbidding reflections—which is effectively what curving the edges accomplishes.)

The files are:

Hat tile

• hat-monotile.svg - A vector graphics file for use in programs such as Inkscape or Adobe Illustrator.
• hat-monotile-kites.svg - A vector graphics file showing the construction of each tile from kites.
• hat-monotile.scad - Code to produce the tile in OpenSCAD, for 3D printing.
• hat-monotile.stl - An STL file produced using the OpenSCAD code, which can be sent directly to a 3D printer, or manipulated in other 3D software.
• hat-monotile.logo - A LOGO script to draw the outline of the title with Turtle graphics.
• hat-monotile.dxf - A DXF vector file, used by some CAD tools. Created by Adam Greenblatt.

Turtle tile

• turtle-monotile.svg - A vector graphics file for use in programs such as Inkscape or Adobe Illustrator.
• turtle-monotile-kites.svg - A vector graphics file showing the construction of each tile from kites.
• turtle-monotile.scad - Code to produce the tile in OpenSCAD, for 3D printing.
• turtle-monotile.stl - An STL file produced using the OpenSCAD code, which can be sent directly to a 3D printer, or manipulated in other 3D software.
• turtle-monotile.logo - A LOGO script to draw the outline of the title with Turtle graphics.
• turtle-monotile.dxf - A DXF vector file, used by some CAD tools. Created by Adam Greenblatt.

Spectre tile

• spectre-monotile.svg - A vector graphics file for use in programs such as Inkscape or Adobe Illustrator.
• spectre-monotile.scad - Code to produce the tile in OpenSCAD, for 3D printing.
• spectre-monotile.stl - An STL file produced using the OpenSCAD code, which can be sent directly to a 3D printer, or manipulated in other 3D software.
• spectre-monotile-outline.scad - OpenSCAD to produce an outline of the tile.
• spectre-monotile-outline.stl - An STL file of the outline.
• spectre-monotile-this-way-up.scad - OpenSCAD to produce the tile with raised text "This way up" on one side.
• spectre-monotile-this-way-up.stl - An STL file of the above.