![]() ![]() Dodecahedron: this is a platonic solid having 12 faces, each of which is a regular pentagon.The PHiZZ module can also be used to create a wireframe model of the torus, by including faces with more edges so as to introduce negative curvature. Graph theorists will recognize them as three-regular planar graphs, and many of our models are also properly three-edge-coloured because our graphs are Hamiltonian. It is useful for constructing wireframe models whose faces are pentagons or hexagons, because those result in sphere-like models. This module is due to Thomas Hull, and is also called the PHiZZ module. Each tetrahedron has six edges, so it took one student 30 units ( Francis Ow’s 60-degree unit) and about nine hours to build this model, following instructions from Thomas Hull’s book Project Origami. This model consists of five wireframe models of tetrahedra, interlaced together. ![]() Five Intersecting TetrahedraĪ tetrahedron is a platonic solid having four faces, each of which is an equilateral triangle. The final shape is built from three identical units, which lock together. This model is due to Molly Kahn, and is an example of modular origami. This model can also become as detailed as your skill allows. Hyperbolic ParaboloidĪnother model from Thomas Hull’s book Project Origami, this model might remind you of a surface from Multivariable Calculus. Self-similar Waveįrom Thomas Hull’s book Project Origami, this is a self-similar origami model and can go on as long as your paper, and skill, permits. When used on somewhat rigid paper, the Miura Map Fold lets you unfold (and refold) your paper by just pulling (and pushing) on a pair of opposite corners.įor more details, visit. Koryo Miura, professor emeritus at the University of Tokyo, developed this fold in the 1970s, as a way of folding things like solar panel arrays so that they could be easily opened and closed for use in spacecraft. A few of the models you will see are listed below, and I will create some more detailed blog posts here for a few of them too, if you would like to learn more. Most of the models were constructed by members of the Association for Women in Mathematics student chapter at UVic and their friends. We hope our mathematical art brightens your December exam period! Visit the classroom wing of the Elliot Building to see a display of mathematical origami starting in early December 2022. 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. Assembly instructions for triakis octahedron (I didn’t print these): Hints and answers to my questions:
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