Dimpled Truncated and Stellated Octahedrons!

Just when you thought you knew me, I figured I'd throw you all a proverbial curveball! There's more to my interests than the Reds (here, here, and here), Baseball in general (here, here, and here), and Baseball Cards (here, here, here, and heck all of these). I also have a second, (less popular) hobby - origami.

That's right, paper folding.

As a mathematician, origami appeals to me because it is all math. Sure, a talented person with an artistic eye can be great at origami - but a person without a single shred of artistic talent can also master origami (which is why I like it)!

Someday I'll probably write about how I got started with origami, but suffice to say, it happened many, many years ago. Over the years, I've purchased a ton of origami books, dabbled in my creating my own origami, and recently, begun the process of figuring out how to turn my origami interests into a PhD dissertation...



I often show off my baseball cards on my blog, but I figured I ought to lend a little exposure to my other hobby as well. The first two models I want to show are from a book titled A Constellation of Origami Polyhedra by John Montroll. In his book, Montroll provides instructions for 34 different origami polyhedra, all made out of a single square piece of paper with absolutely no cutting. The difficulty level ranges from relatively easy (pyramid, octahedron, and a square dipyramid) to the comlex (stella octangula, dimpled snub cube, and gamma star).

One of my long term goals is to fold each of the models in the book - they make a great addition to any mathematics professor's office!


I recently folded two models from the book...

Stellated Octahedron (2 stars - Intermediate):
The stellated octahedron is essentially a cube with the middle of each of the edges pushed in. The resulting shape is a bunch of triangular pyramids in the shape of an octahedron.

The next photo shows how the model is "closed" without any cutting or gluing. John Montroll's design allowed four small flaps to be formed with "extra" paper that are tucked in to lock the entire model. It's quite impressive!

Dimpled Truncated Octahedron (3 stars - Complex):
The dimpled truncated octahedron is made up of 8 sunken hexagonal sides with six small squares connecting the hexagons.



Overall, if you have any interest in origami, I would be more than happy to answer questions! I've folded well over 1,000 models since I began the hobby - including everything from polyhedra to dinosaurs, boxes to sharks, and pretty much everything in between.

I highly recommend A Constellation of Origami Polyhedra, especially if you have either an interest in math or in origami!