UPDATE: This model now makes a PAIR of packable Scutoids, and you can customize various properties and dimensions. In most cases the pair will have two identical pieces that pack together exactly.
There's a new shape in town!
In a new article Scutoids are a geometrical solution to three-dimensional packing of epithelia in the journal Nature, a group of scientists just introduced a new shape that they have dubbed a "Scutoid". Read more at Hacktastic.
This model is CUSTOMIZABLE: Click on the "Open in Customizer" button to get started, then change parameters to suit your needs.
Or, download the demo model, which is particularly nice. A hollow version of the demo model is also included for download. Check out a video of the model at https://www.youtube.com/watch?v=ACk7BCAJDnw. To learn more about scutoids and their shape, watch Matt Parker's excellent explainer and construction video at https://www.youtube.com/watch?v=2_NZ1ql8B8Y.
Don't have a printer, or want something fancy? You can order solid or hollow pairs of these scutoids at affordable 50% scale from our Shapeways shop:
Mathematically, a Scutoid is a Prismatoid to which one extra mid-level vertex has been added. This extra vertex forces some of the "faces" of the resulting object to curve. This means that Scutoids are not polyhedra, because not all of their faces are planar.
In this model, and in the Nature article, the Scutoid has one hexagonal face, and on the flipside, one pentagonal face. In the default configuration of this model, we scaled the faces so that the edges of the hexagonal and pentagonal faces are equal; you can change this scaling in the Customizer. We've also chosen to make the top and bottom faces regular, although biologically that is probably not a requirement. You can download and modify the OpenSCAD code if you want to push the vertices around to make non-regular faces.
For the computational biologists who created/discovered the Scutoid, the key property of the shape is that it can combine with itself and other geometric objects like frustums to create 3D packings of epithelial cells. This 3D-printable model creates two pieces that together pack together exactly.
Apparently this new shape reminded those scientists of the scutellum of a beetle, but obviously it sounds like it should be a Pokemon so @cgreyriley helped me make a card with mypokecard.com. :)
History, thanks, and credit: Thanks to @bpmarkowitz for suggesting that we try to 3D print this model! Kitwallace made a 3D-printable planar-faced version of the Scutoid based on Ed Pegg's vertex coordinates. This model differs in that it has curved sides. One of the images is from an article in The New Scientist.
Disclaimer: I'm not a biologist or a scientist, and the article that announced this shape is pretty technical, so please don't rely on my words above for any Real Science. If you're a scientist who understands this new shape and how it is used, please drop me a note in the comments!
Hacktastic blog: www.mathgrrl.com/hacktastic
Shapeways geekhaus store: www.shapeways.com/shops/mathgrrl
This design has a Creative Commons Attribution Non-Commercial Share Alike license, which means that you can print, remix, and use this model with design credit to mathgrrl, but if you want to sell something then you should ask first, at firstname.lastname@example.org.