We rarely ship a wrong order. However, if we do, we will always take care of the issue for you. If for any reason your order is incorrect, please let us know as soon as possible (within 14 days) so that we can fix your order.

☀️ PLA & The Sun 🌡️

Unless otherwise stated in the listing, my products are printed with a type of plastic called PLA. Do not store items in direct sunlight, or anywhere the temperature will regularly exceed 100°F or the plastic could become soft and begin to warp.

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♻️ Environmental Impact ♻️

PLA, or Polylactic Acid, is a thermoplastic polyester derived from renewable biomass, such as corn starch, sugar cane, or cassava. It is both biodegradable and biocompatible. I also try to minimize waste whenever possible. While I do purchase shipping boxes and bubble wrap, I try to re-use materials as much as I can. As such, your order may arrive in branded boxes from companies I order supplies and parts from. Any packing material apart from bubble wrap (such as air pillows, parchment paper, plastic bags, etc.) is also re-used. Please do your best to recycle shipping supplies whenever possible.

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Price:$16.95+

Spectre Tile Set | Aperiodic Tessellating Tiles | Ein Stein "Hat" Tile Revisited | 3D Printed

Name: Spectre Tile Set | Aperiodic Tessellating Tiles | Ein Stein "Hat" Tile Revisited | 3D Printed
Brand: Filamentality3D
SKU: 1520197300
Availability: InStock
Rating: 5.0 (601 reviews)

Filamentality3D

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Highlights

Materials: 3D filament, PLA

These tessellation tiles are aperiodic, meaning that they can tesselate to infinity without the pattern ever repeating! And unlike their predecessor shape, the Einstein "Hat" tile, these tiles can do so without the need to flip a single tile to their reverse side!

Challenge your mind with your very own set of Spectre tiles! Don't be fooled, though. It's not a easy as it looks!

Makes a perfect gift for children and adults alike! Grab yourself a set (or four) today!

-----------------------------------

--STORY--

In 2023, mathematicians announced that they had finally discovered a single shape that could tessellate forever without the pattern ever repeating itself. They dubbed it the "Einstein" or "Hat" tile. (This is a play on words, as "ein stein" translates to "one stone" in English. It's not actually named after the famous scientist!)

However, there was a catch. Roughly 1 in 7 tiles had to be flipped upside down to accomplish this, and some argued that this meant two distinct shapes were being used. Well, the team of mathematicians kept at it, and only a few months later released a paper describing the "Spectre" tile. This time, they had cracked the code and discovered a single shape that would aperiodically "tile the plane" without having to flip over a single tile!

--SIZE--
Each tile is roughly 2 x 2.5 inches in size.

--COLOR--
If you're looking for a color or colors other than the ones I have listed, just let me know!

--NOTES--
*Shiny silk sets contain 9 different colors, so you will receive 5 tiles of each of the following colors (all silk): Blue, Green, Pink, Purple, Orange, Red, Grey, Copper, Gold
*Please keep in mind that due to the nature of the 3D printing process, this item will have visible layer lines and imperfections on the outer surfaces.

Order today to get by Jun 22-29
Returns & exchanges accepted within 14 days
Cost to ship: $9.54

Enjoy free shipping to the US when you spend $35+ at this shop.
Ships from: Beaverton, OR

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Braden

Owner of Filamentality3D

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Reviews for this item

Buyer highlights, summarized by AI: Great product · Beautiful · Fast shipping · Great colors · Helpful seller · Great quality · Gift-worthy

5.0

(24 reviews)

5.0 Item quality

5.0 Shipping

5.0 Customer service

100% Buyers recommend

5 This item

Etsy buyer Apr 13, 2026

These are great tessellating tiles. We saw this shape at the Mathematics Museum in Manhattan; so happy to find them for our own home!

Etsy buyer Apr 13, 2026

5 This item

Ranchone Mar 4, 2026

Having so much fun coming up with designs using these beautiful tiles! Orders are always sent out ASAP, and Braden is the best about communicating and making sure every order is perfect.

Ranchone Mar 4, 2026

5 This item

Ranchone Mar 4, 2026

Having so much fun coming up with designs using these beautiful tiles! Orders are always sent out ASAP, and Braden is the best about communicating and making sure every order is perfect.

Ranchone Mar 4, 2026

5 This item

Katie Dec 26, 2025

These Spectre Tiles made a really fun gift for a 13-year-old with an interest in math, but we've all be playing with them. They're well-made, they fit together perfectly, and I'm sure they'll last forever. I love the bright colors, but I wish the silver and bronze tiles were replaced with more of the pretty bright colors. Very cool product!