Cookie Cutters - Tileable Shapes (Now with Spectre Monotile!)

UPDATE: New Spectre Monotile!

DESCRIPTION

Another collection of cookie cutters that I've designed over the years.  These are all tileable/tessalation shapes (shapes that can be placed next to each other without a gap) .  They're based around a 50mm default width/length, along with a 2x version.  It's all parametric, so I can always include another size if there's demand.

FEATURES

• 1mm wall thickness with chamfered edge, for reasonable strength while still being good at cutting dough
• sturdy top rim and cross supports for rigidity
• Some models have vertical ribs for additional wall rigidity
• Some models have embossing details, which will impress into the dough without cutting
• Two different sizes
• 15mm depth, which should accommodate pretty much all cookies without using too much filament
• Nearly all internal corner filleted to make cleaning easier

VARIATIONS

NEW!  Spectre Monotile!

David Smith et al just released a pre-publication paper about their newest discovery, a proper Chiral Aperiodic Monotile named “Spectre”.  

The Hat Polykite monotile discovered earlier this year (by the same team) only uses one shape, but the aperiodic tiling of the plane requires mirroring in addition to translation and rotation.  The new Spectre monotile tiles the plane periodically if you allow mirroring, but aperiodically if you DON'T allow mirroring.  In other words, it is a truly chiral aperiodic monotile.  (The paper talks about how you can add s-curves to the sides in order to enforce non-mirroring, but that makes the shape a little too complex for a cookie cutter.  You'll just have to keep all the cookies “right-side-up” after cutting.)

I'll link to the Numberphile video about the shape as soon as it's posted, I'm sure they'll explain it a lot better than I can.  

Here's the paper: https://arxiv.org/pdf/2305.17743.pdf

Hat Polykite Monotile

Discovered in 2023, this is so far the only known aperiodic monotile (that is, a single shape that can tile a plane without repeating the pattern).  It cheaps a little bit, since it actually uses the shape and it's mirror image.  But it's still pretty cool.  It's called the Hat Polykite because it's formed from several connected kite shapes, and it kinda looks like a hat.  

If you want to tile a plane with these cookies, you'll either need to flip about 1/6th of the cookies before baking, or print a mirrored version of the cutter (which you can do in the slicer).

Numberphile Video: 

Penrose Kite and Dart

These two shapes can be used to aperiodically tile a plane (create a pattern that never repeats).  In order to do this, you can only place edges next to each other where the embossed lines also match up.  For ease of recognition, the embossing is at two different heights and thicknesses to distinguish which lines can line up with each other.  

Tesseltree

A shape of my own design (though I'm sure I'm not the first person to come up with the idea), this is a Christmas tree that can tesselate.  It's definitely not aperiodic. But you can get a really dense packing on the cookie sheet.

Sizes

• 1x - 50mm width
• 2x - 100mm width

PRINTING

Material

PLA works just fine, but PETG might resist breakage easier.  ABS could make surface finishing for use with food a lot easier (see below), but I don't have a lot of experience with it myself.

Material Use

4-10 grams, depending on shape and size

Layers/Nozzle

Optimized for 0.2mm layer heights and 04.mm nozzle.  It's possible to print the walls with a single line from a 0.8mm nozzle, but it gets a bit messy.  You want these prints to be as smooth and well-fused as possible for use with food.

Supports

No need for supports or rafts.  You can use a skirt if you have bed adhesion problems, but I haven't needed them

Perimeters and Infill

There is almost no “internal” area in these models.  I'd recommend 2-3 perimeters and 100% infill.  

Other Notes

If you want a specific horizontal size, I'd recommend scaling UP from the smaller model rather than DOWN from the bigger one.  Making the cutting wall much thinner than 1mm can lead to slicing/printing problems, and also gets pretty flimsy.  Scaling vertically should be fine.

POST-PROCESSING

3D Prints and Food

For liability purposes, I cannot recommend that you use 3D prints to prepare or consume food, especially if you plan on washing and re-using them.  3D prints can contain micro-cracks that harbor bacteria, and often warp or deform at the temperatures required to properly clean food utensils.  For that reason, I have not included any pictures of the delicious cookies that I've made with these cutters over the years.

There are several resources on the internet for how to process 3D prints for use with food, usually by coating/finishing them.  I'll leave that as an exercise to the reader.  

VERSIONS

v1 - Initial version

v2 - Added Spectre Monotile

OTHER COOKIE CUTTER COLLECTIONS

Plants, Animals, and Objects: https://www.printables.com/model/499493-cookie-cutters-animals-plants-and-objects

Tileable Shapes (Penrose, Polykite): https://www.printables.com/model/499506-cookie-cutters-shapes

FEEDBACK

I'm more than happy to consider any recommendations or variation requests.  The designs are largely parametric, so if you have a particular size that you need, or depth of emboss or whatever, I'd be happy to include it here.  I'm also happy to add new shapes on request.  These are just the ones I was inspired to make for myself, but they're pretty easy to make once you have all the parameters set up.