The author shows how a modular origami box with a square base can be made from four rectangular sheets plus a template. He also discusses some mathematics in the context of the constructed box.
Diagrams for an icosahedral design made with 30 quick-to-fold units from squares. The look is rather festive, and hence the name. You can fold the with thematic colors of the season to fit right in.
This is the only diagrammed origami model that simulates a true mathematical fractal. It makes a pyramid shape with many branches. No one has yet successfully folded a version without cutting the paper; the version in the picture (folded by the author) was made by carefully cutting the crease pattern into several pieces, folding these using the recursive folding instructions, and then gluing them back together. The challenge of folding recursive diagrams as well as the dexterity involved to not destroy the paper easily put this model in the supercomplex category.
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by Thomas Cooper
There is a family of geometric solids, one of which is illustrated in a famous engraving by Albrecht Dürer, that poses some interesting origami challenges.
An Icosidodecahedron with sunken triangular faces based on a simple unit. Made from 12 pentagons, it is definitely meant for people who like challenges!
During her mathematical studies, Elina Gor researched the changes in complexity of origami models from the 1980`s to the present, to see if we are doomed to face mega-complex models in the future or maybe we already have reached the peak of complexity.
Diagrams for a modular with color change. You can assemble 12 or 30 units. Kami or thicker duo paper is recommended. Scrapbook paper works well, making the result sturdier.
Diagrams for a color-change modular, 12 or 30 units, though like most polyhedral designs, the latter is more attractive. The flower petals are of one color, and the flower centers and background are of another color.
A fun crease pattern that can repeat infinitely to the center folds an octagon into a geometric flower design, where the front and back of the paper look the same.
My origami journey so far, as I celebrate two milestones - 20 years of my online presence and 10 years publishing books. Also find photo instructions for folding Pentas, one of my latest designs.
OrigamiUSA Board member and educator Charlene Morrow reviews a book by Tung Ken Lam and Sue Pope, two experienced British teachers of origami and mathematics.
This is a followup of my previous article, Pentakis Dodecahedron (Issue 35), featuring variation patterns. Mono paper such as copy paper or Tant is a must.
Diagrams for a simple Sonobe type modular made from approximately 1:5 rectangles. This design is great for any leftover strips you may have amassed when sizing paper for other projects.
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by Troels Højer Jensen and Hans Dybkjær
In origami we frequently need to find an \(n\)th of a paper, often in order to divide it into an \(n \times n\) grid. This article generalizes a common technique for finding references and provides some insight into the geometric properties of paper.
The 3-unit Sonobe hexahedron (Toshie's Jewel) and the 12-unit Sonobe octahedral assembly are well known Sonobe constructions. But did you know that you can also construct the former with double the number of units, and the latter with half the number of units, i.e., both shapes from 6 units?
Diagrams for the solid version of the Compound of 5 Tetrahedra aka the 47th Stellation of the Icosahedron, similar to the very popular frame version by Tom Hull/Francis Ow, known as Five Intersecting Tetrahedra or FIT. Some mathematics has been discussed as well.
A quick and easy method of folding a heptagon by Jacques Justin and some related discussions. Francesco Mancini found the method in a pile of letters and notes that he inherited from Roberto Morassi's origami archive.
Tridecagon, also known as the triskaidecagon, is a 13-sided polygon. There are several origami methods already available for folding the tridecagon but the simplicity of my approach may be of interest to people. You may use the tridecagon to transpose origami designs based on other regular polygons.
Toyoaki Kawai’s method of making a pentagon from a square is a widely used one. This article demonstrates how to extend his method to a decagon and shows examples of transpositions of well known designs to pentagons and decagons.
Curved-crease origami can be designed by considering the properties of ruling lines, lines on the crease pattern that remain straight in the 3D folded form. This technique was developed by David Huffman, who identified conic section curves has being particularly suitable for curved-crease designs. Two examples using ellipses are given as crease patterns.
Paper hoarders will appreciate this nifty tool for cutting leftover pieces of paper into common size ratios like 4 by 3, Golden and Silver rectangles, or the ratio of the dollar bill.
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by Thomas Hull
Several variations on a hexagon-based, iso-area, geometric collapse method are shown. Some of these were taught at the 2013 OrigamiUSA Annual Convention in New York City.
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by Arnold Tubis and Carmen Sprung
Tubis and Sprung show that the same starting shapes used previously to create generalized masu boxes [Tubis and Pooley 2012] can be used to produce \(n\)-pointed 3D stars.
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by Arnold Tubis and Christopher Pooley
Tubis and Pooley explore \(n\)-sided generalizations of the masu and one of its many decorative-lids. Detailed video instructions are provided at the Origami Player site.
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by Arnold Tubis, John Andrisan, and Christopher Pooley
Paper folding exercises involving the golden section of a line, the golden rectangle, and the golden triangle provide interesting geometry-teaching supplements.
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by Arnold Tubis and Crystal E. Mills
A method for making four-compartment side–to–side or corner–to–corner divider inserts for prism-shape containers with square faces is generalized so as to produce n equal compartments of specified height for a container with an n–sided regular-polygon face.
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Arnold Tubis
Two conundrums concerning the Betsy Ross Five-Pointed Star: the provenance of the Pattern–for-Stars artifact and the surprising incompleteness of fold and one-cut descriptions for making the star.
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Thomas Hull
The names Maekawa and Kawasaki are known to origamists as great origami creators. But did you know they have Theorems named after them too? And so does the French paper folder Jacques Justin. See what these Theorems are all about. Warning: Math ahead!
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By cmorrow [at] mtholyoke.edu (Charlene Morrow)
An expanded version of a 5OSME convention commentary that appears in the Winter 2011 issue of The Paper, pp 18-19. Many more interesting experiences and color photos that could not be included in The Paper version due to limited space.
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by Tom Hull
The origami wind spinner is a traditional, if somewhat obscure model of repeated pleat folds. We ask ourselves, "What kind of shapes can paper form with these simple pleats?" and, "How much can we make a square piece of paper rotate with this pleating scheme?" The answers are surprising and fun!
At the recent 5OSME convention, an impromptu challenge involved incorporating a "nonexistent" fold, the origami hypar, into definitely existent origami models.