# Posts: mathematics

#### Polypolyhedra in Origami

These images show what the (first) 54 polypolyhedra would look like if created using the Ooh and Ow unit joints (Ow being Francis Ow’s mechanism for joining struts at angles up to 90 degrees, Ooh being my own similar mechanism for larger angles). Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. […]

Continue Reading#### Polypolyhedra in Dowels

These images show what the (first) 54 polypolyhedra would look like if created using round dowels of the maximum possible diameter. Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. Polypolyhedron 7. Polypolyhedron 8. Polypolyhedron 9. Polypolyhedron 10. Polypolyhedron 11. Polypolyhedron 12. Polypolyhedron 13. Polypolyhedron 14. Polypolyhedron 15. Polypolyhedron 16. Polypolyhedron 17. […]

Continue Reading#### Polypolyhedra

Background In 1999, I became interested in a family of origami modulars composed of interwoven polygonal frames and/or polyhedral skeletons, the most famous of which was devised by Tom Hull, which he titled Five Intersecting Tetrahedra, now commonly known by its abbreviation, FIT. (See here for a description.) The underlying polyhedron—a compound of five tetrahedra […]

Continue Reading#### Science Links

This page contains various and sundry links to web pages that combine origami with mathematical or scientific applications. See here for additional links not specifically related to mathematical and scientific origami. Please let me know if you find any broken links or if there are any pages you think I’ve overlooked. Origami Mathematics Tom Hull’s […]

Continue Reading#### Origami Conferences

Since 1989, there have been several highly successful international scientific conferences exploring the interactions between origami, mathematics, science, and (since 2001) education. The conferences take place at irregular intervals—basically, whenever a general chair and sponsoring organization decide that the time has come for the next. Beginning in 2015, the OSME series of conferences is guided […]

Continue Reading#### 4OSME

2006-10-16 Update: 4OSME was a rousing success! Over 165 people attended some 70 talks. The 4OSME proceedings has been published by A K Peters, Ltd (now part of CRC Press). Several media groups covered 4OSME. See photographs and a trailer from Green Fuse Films’ Peabody-award-winning documentary on origami (portions of which were filmed at 4OSME), […]

Continue Reading#### Angle Quintisection

This figure shows the key step in performing an origami angle quintisection—division into equal fifths—by folding alone. Within the mathematical theory of origami geometric constructions, the seven Huzita-Justin axioms define what is possible to construct by making sequential single creases formed by aligning combinations of points and lines. It has been mathematically proven that there […]

Continue Reading#### Huzita-Justin Axioms

At the First International Meeting of Origami Science and Technology, Humiaki Huzita and Benedetto Scimemi presented a series of papers, in one of which they identified six distinctly different ways one could create a single crease by aligning one or more combinations of points and lines (i.e., existing creases) on a sheet of paper. Those […]

Continue Reading#### OrigamiUSA’s The Fold

Starting in November, 2010, I began writing a regular column on crease patterns (with occasional forays into other topics) for OrigamiUSA’s then-new online publication, The Fold. You’ll need to be a member of OrigamiUSA to read the articles, but in my highly biased opinion, it’s well worth the cost (not just for my articles, but […]

Continue Reading#### ReferenceFinder

Background During the development of technical folding that began in the 1980s, a new problem arose for the origami designer: how to find the major creases in the base by folding alone. This didn’t used to be a problem. In the traditional “trial-and-error” approach to origami composition, the design was discovered via exploration of folding. […]

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