Articles for keyword: geometric

Diagrams: Poinciana

A model from Meenakshi’s new book.

Diagrams and Video: A Triangular Gift Box

by Arsalan Wares
A sturdy modular box and the mathematics behind it.

Once Upon a Time in Versailles: Part 1

by Krystyna Burczyk and Wojtek Burczyk
Musings on art, kitsch, mathematics and the creative process. And lots of diagrams.

Once Upon a Time in Versailles: Part 2

by Krystyna Burczyk and Wojtek Burczyk

Diagrams and Video: Balloon Box

A two-piece icosahedron that’s a gift box and an ornament.

Diagrams: Festive Icosahedron

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.

Diagrams: Fractal Pyramid

by Ushio Ikegami
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.

Truncated Trigonal Trapezohedrons and Special Pentagons

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.

Icosidodecahedron

An Icosidodecahedron with sunken triangular faces based on a simple unit. Made from 12 pentagons, it is definitely meant for people who like challenges!

Diagrams: Fractured Star

A one-piece star that gives the appearance of being made of multiple diamonds. If you like tessellations (or not), this should be fun to fold.

Diagrams: A Ring and a Kusudama From the Same Unit

by Krystyna Burczyk

Diagrams: Magic Square Cash

A simple, decorative modular — best made from heavy, smooth paper — that slides to changes shape.

Diagrams: Windmill Flower

by Mahyar Hossien Khani
An ingenious combination of two origami forms.

Diagrams: Star Arisa

by Nobuko Okabe
You'll need 8 squares to fold one of 12 variations of this versatile, modular star.

Diagrams: Star Ypóthesi

Grab 8 squares to start folding this wonderful modular star.

Diagrams: Double-Sided Two-Tone Diamond

A double-sided spiral diamond from one sheet of paper. Sy Chen based this design on his earlier two-tone diamond, which appears on the OrigamiUSA website. Links to both models are in the article.

Diagrams: Two of Hearts

by Francesco Mancini
Valentine’s day is coming, and if you like origami hearts and you’re also into modulars, you can follow the diagrams and fold a Two of Hearts modular.

Diagrams: Poinsettia With Leaves

A Fujimoto-inspired poinsettia with leaves looks great in red-green duo paper, but you could use green paper with a white back to fold a rare white poinsettia.

Diagrams and video: Winter Star

by Jane Rosemarin
These four stars from one basic design were created to pop in an envelope and mail.

Diagrams: Asturo Star

by Usman Rosyidhi
The Asturo Star is a new modular by the Indonesian designer Usman Rosyidhi. It's an elegant model that's easy to fold and assemble.

Diagrams: Hexagonal Flower

Diagrams for a flower folded from a hexagon. Like many polygonal designs, the flower can also be transposed to pentagons, heptagons, and octagons. Also includes how to fold a hexagon from a square.

Diagrams: C-fold Fish Hook Module

by Craig Hunter
Diagrams for Fish Hook Module with details of how to build a cube and an octahedron. The modules are edge modules, and most polyhedra can be built, except those that have five or more edges meeting at a vertex.

Diagrams: Stella

After teaching Stella for Origami Connect, Evan Zodl agreed to write an article for The Fold to make this lovely model accessible to more people.

Diagrams: Twist Antiprism Box

Christiane Bettens presents us with another variation of an antiprism box.

Diagrams: Delicata

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: Verbena

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.

Crease Pattern: Octagonal Iso-Area Self-Similar Flower

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.

Diagrams: Sierpinski 3D Fractal

Paolo Bascetta presents us with a creative, new Sierpinski 3D fractal created by stacking.

Diagrams: Pollen Kusudama

by Mukul Achawal
Diagrams for a color-change modular made from 30 rectangles.

Diagrams: Stella Lefty

Here are diagrams for Stella Lefty by Francisco Mancini, taught by Char Morrow at the 2018 OrigamiUSA Convention.

Diagrams: Spinning Shooting Star

by Nobuko Okabe
Nobuko Okabe presents a spinner made from one square.

My Origami Story

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.

Diagrams: Penrose Triangle

Alessandro Beber presents us with a simple origami version of the Penrose triangle: "impossibility in its purest form."

Story of the Paper Ticket Steam Engine

Winnie Leung provides instructions for building a steam engine and offers to equip you with the necessary paper tickets.

Diagrams: Blooming Fractal Flower

by Joanna Sobczyk, diagrams by Adam Szewczyk
Diagrams for a beautiful fractal flower from a hexagon with color change. A very advance design for someone who has only been folding since 2013.

Diagrams: Little Flowers

by Meenakshi Mukerji
Diagrams for a 30 unit modular with color-changed five petaled flowers. For four petaled flowers assemble 12 units.

Diagrams: Rose Quilt

by Usman Rosyidhi
Diagrams for the Rose Quilt, by Usman Rosyidhi, from Indonesia.

Crease Pattern: Distorta2016

Here is Distorta2016 by Alessandro Beber.

Exhibit: Tsunagu Gallery Meets Tomoko Fuse

For your enjoyment, here are photos from a small exhibition of Tomoko Fuse's art at the Tsunagu Gallery in Tokyo.

Crease Patterns: Distorta2009

Here are some crease patterns for a number of Alessandro Beber's beautiful high intermediate creations.

Diagrams: Whirlwind

Diagrams for a simple modular from 2:1 rectangles, released in open access to celebrate the World Origami Days 2016.

Diagrams: Patterned Pentakis Dodecahedra

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: Mercapton Dodecahedron

by Mukul Achawal
Diagrams for a 30 unit modular dodecahedron with color change by Mukul Achawal of India.

Diagrams: Pentakis Dodecahedron

Diagrams for a simple modular from squares 4" or smaller. For larger constructions though, use paper of proportion $$5:3\sqrt{3}$$, i.e., $$1:1.039$$.

Crease Pattern: Propellers Tessellation

An exploration of a propeller tessellation formed from standard square twists.

Diagrams: Vidrio

Photo diagrams for a 30 unit modular with subtle curves by Aldos Marcell of Nicaragua. Assemblies with other number of units possible as well.

Diagrams: Posy Sonobe

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.

Diagrams: Spring Beauty

Diagrams for a 12 or 30 unit modular with color change. The starting paper size ratio for an unit is 1:3.

Theme and Variation

by Thomas R. Crain
This article explores several variations in a square twist crease pattern that may be achieved simply by varying the mountain/valley assignment of the same underlying crease pattern.

Diagrams: Gemstone Sonobe

Diagrams for a 30-unit Sonobe type design with color change. Other assemblies such as 3, 6, 12 or larger number of units are possible as well.

Diagrams: Regulus Kusudama

Diagrams for a 30 unit modular design.

Diagrams: Pentagonal Bowl Spin

Diagrams for a spinable top by Ali Bahmani, folded from a pentagon.

Diagrams: Ice Star

Diagrams for a simple 5 or 6 unit sturdy modular design.

Diagrams: Star of Wonder

Diagrams for an octagonal star with color change, from a single uncut square. Also included is a variation of the star.

Orange Spheres and Odd Even Apples

by Hans Dybkjær
This article tells the tale of the higher spheres of oranges and apples: How I got there, and how to make them.

Introducing Building Block Units

Building Block Units (BBU) are a new family of modular origami units, with over one hundred different interlocking module designs.

Diagrams: Winged Heart

by Nguyen Quang Do Lisa
Diagrams for a heart with wings designed by Nguyen Quang Do Lisa.

Diagrams: Two Unusual 6-unit Sonobe Constructions

by Meenakshi Mukerji & Ittai Hacohen
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: Lucia

Diagrams for a floral modular designed by Ekaterina Lukasheva.

The Lesser Known Twin of The Sonobe Unit

A discussion of an alternate Sonobe Unit assembly which produces a surprisingly different result than the conventional one. Diagrams included.

Diagrams: Crape Jasmine

Narong Krined
Diagrams for a beautiful 12 or 30 unit Sonobe Variation.

Diagrams: Dollar Box and Duck

by Milind Oka
Diagrams for two money fold models, a box with lid and duck, by Milind Oka.

Crease Pattern: House with Windows

by Clifford Jones
A progressive crease pattern for a box-pleated house with latticed windows by Clifford Jones.

Diagrams: Pinwheel Flower Ball

Diagrams for a beautiful 12 or 30 unit modular.

Folding Wood

The story of a process developed for folding rigid wood laminate, with crease patterns, images, and recipes.

Diagrams: 3D Tree

Diagrams for a geometric, two-sheet, 3D tree for the holiday season.

Diagrams: Compound of 5 Tetrahedra

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.

Diagrams: Marquise

Diagrams for a 30-unit modular design by Ekaterina Lukasheva.

Editorial: Dear Roberto...

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.

Diagrams: Decorative Cubes

Diagrams for various decorative cubes based on Froebel designs applied to blintzed windmill bases.

Diagrams: Setting Sail

by Joseph Fleming
Diagrams for a Sailboat on the sea by Joseph Fleming.

Diagrams: Hearty Cube

Diagrams for a 6 unit cube with hearts on all faces and two specially colored diagonally opposite vertices. 24-unit assemblies are possible and left as challenge.

Diagrams: Ice Queen

Diagrams for a 30-unit modular design by Ekaterina Lukasheva of Russia.

Diagrams: Rona Star

Diagrams for a simple, eight-piece modular ring.

Editorial: Folding the Tridecagon, that Odd Polygon

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.

Diagrams for a 30 piece modular design by Natalia Romanenko of Moldova.

Editorial: Annals of Early Origami

The origins of origami in Japan are lost in the mists of history, but we have surprisingly good records of paper-folding from over a thousand years ago in pre-Columbian Mesoamerica.

Diagrams: Nymph

Diagrams for a 30-unit modular design by Ekaterina Lukasheva of Russia.

Editorial: Star Block Variations

A sunk-side elbow design is used to create a variety of models: Star Block models in particular. This method has the potential for much creative work!

Diagrams: Two-sided Sakura Star

Diagrams for a Sakura Star by Ali Bahmani designed to be viewed from both sides.

Editorial: Extending Kawai’s Pentagon Method to a Decagon

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.

Diagram: Sonobe Capuchona

by Irina Reutskaya
Diagrams for a 30-piece modular design by Irina Reutskaya of Russia.

Diagrams: Magic Ninja Star

Diagrams for a two piece modular star designed by Sy Chen that can rotate to change form.

Diagram: Kusudama by Daniel Reutsky

by Daniel Reutsky
Diagrams for a 30-piece modular design by Daniel Reutsky of Russia.

by Nobuko Okabe

Design: Folding Pictures

An article about folding images using large grids and hundreds of reverse folds.

Diagrams: Mountains

by Herdy Soepono
Diagrams for two simple connected mountains by Herdy Soepono.

Diagrams: Karlsson Kusudama

Diagrams for a 30-piece modular design by Valentina Minayeva of Ukraine.

Diagrams and Video: Hex Star

Diagrams and video for a 6 piece modular star by Maria Sinayskaya.

Nomograms: Determining Paper Sizes Made Easy

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.

Diagrams: Simple Modular Square Pyramids

by Thomas E. Cooper
Diagrams for a simple pyramid model with variations, used for to help teach geometry.

Diagrams: Dulcinea

Diagrams for a 30 piece modular by Uniya Filonova of Russia.

Diagrams: Giant Star

Diagrams for a 8 piece modular star by Maria Sinayskaya of South Africa.

Framing George Washington II

by Arnold Tubis
Arnold Tubis offers yet another dollar bill fold of George Washington, framed on both sides of the model using two dollar bills.

Cool Iso-area Hexagon Collapses

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.

$$N$$-Sided Closed Masus

by Arnold Tubis
A folding method for closed masu boxes from a single square, generalized to masu-like structures with regular polygonal bases.

Diagrams: Starfruit

Diagrams for a 30 piece modular design by Natalia Romanenko of Moldova.

Designing and Folding Curved-Crease Pleated Forms

This article aimed at novice folders examines the design and folding process for geometric bowl and vase models characterized by a series of curved pleats.

Diagrams: Ace of Diamonds

Diagrams for a simplified color-change diamond playing card symbol by Meenakshi Mukerji.

Crease pattern: Hexonion

A rotationally symmetric solid curved fold, folded from a regular hexagon.

Diagrams: Star Hilli

Diagrams for a modular star "Hilli" by Klaus-Dieter Ennen, as well as video instructions by Sara Adams

Diagrams: 8 Pointed Flowery Star

Learn how to fold the first in a series of many variations on a single star. This one has eight points, but you can achieve any number from 3 to 12 using this method.

Diagrams for the 2012 OrigamiUSA Holiday Gift.

Diagrams: Double Star Puff Pyramid

Diagrams for a 3D Double Star Puff Pyramid folded from a regular hexagon.

Folding a Golden Gnomon Box

by Arnold Tubis, John Andrisan, and Christopher Pooley
Part two in a series examining the mathematics behind the golden ratio in some geometric boxes.

Interview: Daniel Kwan and Byriah Loper

by Wendy Zeichner
An interview with two pioneers of modular woven polypolyhedra.

Diagrams: Curled Sonobe

A simple yet elegant Sonobe variation by Meenakshi Mukerji.

A Class of $$N$$-Pointed 3-D Stars

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.

Six Intersecting Pentagrams: Diagrams and the Puzzle of Its Genealogy

Diagrams for the model Six Intersecting Pentagrams, plus an article on its history.

Modular Origami: the DeZZ Unit

Learn to fold a family of modular units that can create a wide variety of deltahedra, polyhedra whose faces are equilateral triangles.

Math: Trisection Construction Proof

by Bennett Arnstein
Proof of Lewis Simon's construction for the trisection of the side of a square or the short side of a rectangle.

Generalized N-Sided Masus

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.

Five Intersecting Octahedra

Meenakshi Mukerji
30 pieces of paper are folded to make a modular version of the Compound of Five Octahedra model.

Cutting Paper with Origami

by Ilan Garibi
Can you cut paper with origami instead of scissors? While trying to design a 24 unit Stellated Octahedron, I got stuck with all the math involved and decided to make it simple - cut the intersected units by folding.

Folding Waves, Part 1

Thomas Hull
This wave model is fun to fold and has a lot of math in it!

Diagrams: Heart Variation

Diagrams for a heart variation based on a model by Edwin Corrie.

Crease Pattern: Wave24

A pleated cone sliced by multiple planes creates this geometric model reminiscent of a breaking wave.

Diagrams: Burr Puzzle

Diagrams for a classic puzzle, typically made of wood.

Diagrams: Double Sided Star of David

by Ilan Garibi
Diagrams for a Star of David from 6 units.

Crease Pattern: Trees

Crease patterns and video for two modular tree units with variations.

Crease Pattern: Hexabox

A rotationally symmetric geometric shape, folded from a hexagon, based on Jeannine Mosely's "Bud".

Diagrams: 12 Pointed Star & Square Squared

Diagrams for two modular designs.

How to Prove that Origami is Hard

by Tom Hull
A summary of Bern & Hayes' proof that flat-foldability in origami is computationally hard!

Modular Design: Shishapangma

Design and folding instructions for one of the 54 polypolyhedra using dollar bills.

Diagrams: Color Shifter Duo Star

Diagrams for an elegant seven piece color-change modular.

Diagrams: Hiccius Doccius

Diagrams and video tutorial for a color-change box modular.

Divider Inserts for N-sided Boxes

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.

Crease Pattern: Honeycomb

With many tessellations, the obvious way to design the crease pattern doesn't necessarily result in a foldable pattern. By adding extra creases to the pattern, you can sometimes find an alternate way to the finished form, as you'll see in this geometric pattern.

Diagrams: Stardust

by Didier Piguel
Diagrams for Didier Piguel's Stardust, a star that can be transformed into an abstract yet expressive character.

Beyond the High-Tech Side of Origami: What I Learned at 5OSME

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.

Geometric Folding Algorithms: Free Video Lectures

Course information for an MIT graduate course in Geometric Folding Algorithms.

Tessellations: A Brief Theory of Warping Paper

This article gives a nice overview of the types of tessellations there are, and how to create one yourself.

Pureland Origami: Clarity Through Simplification

by Andrew Hudson
Pureland Origami is used as the starting point for a discussion about realism and convention vs. simplicity and clarity in diagramming style