This model used up my entire supply of old University of Minnesota business cards to make the Level 1 sponge we will need another 2,280 business cards. Instructors in any class using this activity should be forewarned that it is normal for students to become addicted to making business card cube structures.įor our final mathematical paper folding project of December, we assembled a Level 1 Menger Sponge model: Our level 1 Menger Sponge, built out of 120 business cards. In his book Project Origami, Thomas Hull gives instructions for folding models of portions of the Menger Sponge out of business cards. If you haven’t see those other things then this is a good opportunity to spend some quality time on Wikipedia. The Menger Sponge is a three-dimensional fractal curve if you have seen the Cantor Set (in one dimension) or the Sierpinski Carpet (in two dimensions), the Menger Sponge will look familiar to you.
Thank you to Arif Babul (Physics & Astronomy) and Duncan Johannessen (Earth & Ocean Sciences) for the donations! Author Jane Butterfield Posted on DecemFormat Video Categories Origami Tags origami Leave a comment on Miura fold Menger sponge I will also add some examples made from geological survey maps, donated by a colleague from Earth & Ocean Sciences, because the Miura fold is also excellent for storing maps.
Modular origami pinwheel instructions update#
I will update the Elliot Building displays soon, to include this space-themed example. In this video, you can see me demonstrating the two-points-of-contact folding and unfolding that the Miura fold provides: Click on the picture to watch the video. Because of this space connection I asked a colleague from Physics & Astronomy to donate something more space-related for me to fold, to replace the math research poster I had originally used for our display.
Since our first assembly of the display, I have made several more!Īstrophysicist Koryo Miura developed this fold as a way of packing things such as solar panels flat, so that they could be very easily opened (and closed) in space. You can see some examples of this fold in the Elliot Building origami display ( here is a link to my post about that). It is harder to properly three-colour the triakis icosahedron, though! For the triakis octahedron and the triakis icosahedron, three colours suffice (the triakis icosahedron pictured below is properly three-coloured).An icosahedron has 20 faces, each of which is replaced by a trio of Sonobe units, and each unit participates in two faces, so you need 30 pieces of paper.The “cube” is actually a “triakis tetrahedron”, so it’s not as special as it seems! This might take some drawing to work out you might find it helpful to imagine what is left over if you slice each vertex off of a cube.You’ll need at least three colours for any of these models, because Sonobe units lock together in trios.How many faces has a cube got? Second way: each triple of Sonobe modules is going to form the corner of a cube how many corners is each module involved in, and how many corners has a cube got? There are at least two ways to count it! First way: each Sonobe module is going to end up with its square inner bit being the face of a cube. This one is a dodecahedron-shaped (30 units), but a 90-unit truncated icosahedron should also be possible.Assembly instructions for triakis octahedron (I didn’t print these): Hints and answers to my questions: I only learnt this after I started making these structures, so not all of them have this optimal colouring! The same 3-colour rule is true for the other Platonic solids, and also for the truncated icosahedron.įrancesco Mancini’s star-holes kusudama uses a similar module to the PHiZZ, but with a little back-bend that gives a nice 3D star effect. It’s fairly easy to work out which edge in the 2D diagram correspond to which edge in the thing you’re building.If you colour alternate edges of the Hamiltonian circuit in two of your chosen colours, and the rest of the edges in the third, then you’ll avoid having any colour-clashes. The diagram is a projection of a dodecahedron: imagine taking a wireframe of the dodecahedron and shining a torch through it: the Schlegel diagram is the 2D shadow this 3D polyhedron casts on the wall. You’ll notice that every vertex has one of each of the three coloured edges. The red and purple edges form the Hamiltonian circuit the grey edges are what is left over. Hamiltonian circuit through the Schlegel diagram of a dodecahedron.
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