Do you want to make beautiful 3D-printable sculptures, jewelry, and lamps? It’s easier than you might think — if you know how to use TopMod. TopMod is a really unique tool to have in your 3D printing toolbox. It specializes in remeshing, wireframing, stellating, and modifying object meshes, and by combining those powerful functions you can quickly create stunning 3D-printable works of art. And, if you love beautiful mathematics, we’ll have some of that for you in this post as well!

For example, you could start with a dodecahedron cell, add stellations to the faces, and then remesh to smooth everything out, like this:

### Topology

In mathematics, topology is the study of shapes or objects that are preserved under certain deformations. In other words, to a topologist, two objects are considered the same if one can be continously morphed into the other without breaking, tearing, or gluing. So a topologist can’t tell the difference (and doesn’t want to tell the difference) between a cube and a ball, or even between a donut and a coffee mug. To see this principle in action, check out Henry Segerman’s Topology joke video on YouTube, or even buy a 3D-printed version of the donut-to-coffee-mug sequence at his Shapeways store.

If you’re feeling even more mathy than that, and want to see some current academic research, take a look at Ergun Ackleman‘s  papers on topological mesh modeling.  Dr. Ackleman is Professor at Texas A&M University, and also, not coincidentally, the creator of TopMod.

Or, if you just want to get to the modeling, here’s how topology is relevant to you: Sometimes you want to create a basic rough outline shape for an object, and then later smooth, morph, or transform that object. When you do that, you’re doing topological mesh modeling; you’re changing how the object sits inside three-dimensional space, but not changing the fundamental character, or topology, of the object. Or, sometimes you want to add “extra topology” to an object by creating new holes or connections. Either way, TopMod can help you do it quickly and easily.

### Getting started with TopMod

So, what can you make with TopMod? Here’s a beaufiul example: an intricately wireframed Golden Superegg Mesh by microcubology. A superegg is a special type of superellipsoid, which is a 3D object whose cross-sections are superellipses, and the “golden” in the title refers to the Golden Ratio. In this model, TopMod was used to create the mesh pattern on the surface of the superegg, and then to convert that mesh to a wireframe.

To get started with TopMod, including how to use basic geometric obejcts and apply its rind modeling and remeshing functions, check out this ShotGlass TopMod Tutorial by Mathieu Glachant. One pro tip if you find you’re unable to move around in TopMod: To navigate in TopMod you have to hold down the “option” key while moving around with your mouse.

### Loops and Crusts

With TopMod, it’s easy to create complex mathematical objects that look great as jewelry, such as this Split Mobius Band, made by Skeletal Skulpture and Mathematikal Artifakts. This design is basically a torus (that is, a “donut”) that has been hollowed out around a ring of faces that spiral around the mesh of the object.

To see how to make objects like these, check out this beginner’s TopMod Tutorial by PinkPanthress on YouTube. In this video, you’ll see nearly the same process that was used in the model above, except with a figure eight shape (actually, a “double torus“) instead of a torus.

For something truly amazing, take a look at purligar’s beautiful Starfish Lamp,. You can turn this 3D print into a pendant lamp by also printing an Adapter Ring, or make it a standing lamp as shown below with the Starfish Lamp Stand.

The Intermediate Star Ball Tutorial by Gravitomag walks through the creation of exactly this star formation in TopMod, by extruding faces cut from a dodecahedron and then connecting them with topological handles. (Math geek note: In this case we are changing the topology of the object; in fact, mathematically, adding and removing handles is a key way to change topology.)

Have you used TopMod to create 3D-printable objects? Add links to your creations in the comments so we can check them out! Or, if you’re just getting started with topological mesh modeling and have questions, ask us here and we’ll do our best to answer. (Or, if you want to geek out and talk math, we’re up for that too!)