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Marvelous Modular wildlifeprotection.info 18/13/ PM Jasmine Dodecahedron 1 (top) and 3 (bottom). (Se. Marvelous Modular Origami by Meenakshi Mukerji. Clockwise: Module Decoration Box from 2xls adapted from dollar bills. Module Dodecahedron from degree module from 4x3s. Module Decoration.

Marvelous Modular Origami Pdf

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Download as PDF, TXT or read online from Scribd. Flag for inappropriate content . Marvelous Modular Origami Meenakshi Mukerji A K Peters. Natick. in such a way as to create magnificent three-dimensional structures without the use Modular origami isn't limited to polyhedra—flat stars, coasters, tessellated . The Sonobe unit is one of the foundations of modular origami. There are many variations . Reference: Book: Marvelous Modular Origami by Meenakshi Mukerji.

Width will vary proportionately with model. Everything works except highly glossy paper need a little friction to hold. Foil paper produces the best locks. Finished Model Size Paper 4. Fold and open centerlines. Match dots to form new creases as shown. Crease and open corners. Fold and open along existing creases behind. Valley fold and open as shown, then mountain fold pre-existing crease.

Tab Note that a tab-pocket pair is at the back. Firmly crease the two units together towards the left as shown in the enlarged inset, thus locking the units. Assembly 7 6 2 1 3 5 4 Let each bent line represent one unit. Assemble 5 units in a circle to form one flower, following the sequence numbers.

Then insert a sixth unit doing Steps 6 and 7 to form one hole. Continue building 12 flowers and 20 holes to arrive at the finished model. Pinch halfway points as shown, then recrease cupboard folds. Crease and open to match dots. Inside reverse fold corner. Repeat Steps 7 and 8 on the reverse side. The last two reverse folds will overlap. Pocket Tab Insert tab into pocket. Note that a tab-pocket pair is at the back. Assemble as explained in Poinsettia Floral Ball to arrive at the finished model.

This diagram uses 2: Start with 2: Fold and open equator. Then pinch top and bottom of center fold. Match dots to form new creases. Fold and open corners, then valley fold preexisting crease.

Valley fold and open along pre-existing crease. Repeat behind. Inside reverse fold along existing creases. Tab Pocket Note that a tabpocket pair is at the back. Locking Insert tab into pocket. The resultant diagram is shown with truncated units. Note that the locks in this model are hidden. Pinch ends of center fold and equator, then do Steps 2—6 of Plumeria Floral Ball. Mountain fold and open corners, then curve unit gently towards you, bringing top edge to the bottom.

Exquisite Modular Origami

Release curve and insert tab into pocket. Curves will reappear during assembly.

There will be tension in the units so you may use aid such as miniature clothespins which may be removed upon completion. Insert tab inside pocket.

I first stumbled upon an origami patterned dodecahedron by chance in a Japanese kit that consisted of 30 sheets of paper and directions, all in Japanese—but that is the beauty of origami, it is an international language! The only problem was that I could not read who the creator was. Sometime later I came across some beautiful patterned dodecahedra by Tomoko Fuse. Thanks to them all for providing me with the inspiration to create some patterned dodecahedra of my own.

All models in the dodecahedra chapters are made up of 30 units with one unit contributing to two adjacent faces of the dodecahedron. Everything works. Finished Model Size 4" squares yield a model of height 4. Pinch ends of center fold, then cupboard fold. Fold and open top two layers only. Reverse fold corner along pre-creased line from Step 4. Pinch flaps halfway. Repeat Steps 4—7 at the back. Tuck corner back along pre-creased line. Open mountain fold from Step 3.

Lock two units together by tucking back along crease made in Step 5. Form one face of the dodecahedron by assembling five units in a ring in the order shown. The last two units will be difficult to lock; the last one may be left unlocked. Assemble sixth unit as shown to form a vertex.

Continue making faces and vertices to complete the dodecahedron. Start with Step 9 of the previous model and tuck marked flap under. Pull corner out from behind. Turn over and repeat Steps 1—3. Pocket Tab Assemble units as in previous model to arrive at the finished model.

Note that locking gets difficult in this model. Tab Assemble units as in previous dodecahedron to arrive at the finished model below. Use paper of the same size for the template and the units. Four-inch squares will yield finished models about 4" in height. The template will also be cre- ated using origami methods.

The use of a template will not only expedite the folding process but it will also reduce unwanted creases on a unit, making the finished model look neater. Making a Template 2 2.

Valley fold top layer only. Pull bottom flap out to the top. Fold into thirds following the number sequence.

Mountain fold at center. Turn over and repeat. Open mountain fold from Step 5. Unfold crease from Step 6 and repeat at the back. Mountain fold along edge of back flap. Valley fold to match dots.

Valley fold tip. Unfold Steps 13 and Finished Template Unit Repeat Steps 12—14 at the back and then open to Step 5. Then, fold 30 units following the diagrams below. Use same size paper for the template and the model.

Lay on template and make the mountain creases. Fan fold into thirds following number sequence. The portion above CD helps lock units together. Continue assembling faces and vertices as in Daisy Dodecahedron to arrive at the finished model. Crease and open center fold. Then valley fold into thirds and open.

Repeat on DC. Mountain fold to re-crease portions of the flap shown. The lock of unit 2 will lie above line BC of unit 1. Crease center fold. Valley fold flaps as shown.

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Mountain fold as shown. Mountain fold to re -crease the portions of AB and CD shown. Snip with scissors along the dotted lines, approximately less than half way from A to B. The lock of unit 2 will lie above line BC. Continue assembling as in Daisy Dodecahedron to arrive at finished model. Valley fold each edge twice. Valley fold existing creases. Mountain fold to re-crease the portions of AB and CD shown. Assemble as in Daisy Dodecahedron to arrive at the finished model.

Assemblies shown in regular and reverse colorings. Mountain fold corners and tuck under flap. Valley fold corners, top layer only. C Pocket Finished Unit Assemblies shown in regular and reverse colorings. Do Steps 1 through 7 of Swirl Dodecahedron 1. Valley fold to match dots and repeat on the back.

Re-crease mountain fold shown. Open mountain fold from Step 8. Perform Steps 10 and 11 of Swirl Dodecahedron 1 to form locks. The Lightning Bolt and the Star Windows are essentially Sonobe-type models, but, unlike Sonobe models, they both have openings or windows.

It was only when someone asked me if I was inspired by the Curler Units that it first came to my attention. Although the models seem similar at first glance, they are really quite different, as you will see.

The Curler Units are far more versatile than my Twirl Octahedron units. With the former you can make virtually any polyhedral assembly, but with the latter you can only make an octahedral assembly. Start with A 4 paper. Pinch ends of centerline, then crease and open the diagonal shown. Pinch halfway points as marked.

Fold to align with diagonal crease from Step 1. Fold to align with existing diagonal crease from Step 1. Fold to bisect marked angles. Open last three creases. Repeat Step 11 on the back. Unlike Sonobe models, pyramid tips will be open. You can also make models out of 3, 6 , 12, or more units.

Use same size paper for both Twirl and Frame Units. Twirl Units 3. Valley fold and open top flap only. Fold one diagonal. Mountain fold rear flap. Open last two folds. Make curl as tight as possible. You may keep curls held with miniature clothespins overnight for tighter curls. Fold small portions of the two corners shown. Crease and open like waterbomb base. Finished Frame Unit 3. Collapse like a waterbomb base.

Note that Step 2 is optional: Making one face of the octahedron. To form one face of the octahedron, connect three Frame Units and three Twirl Units as shown above.

Continue forming all eight faces to complete the octahedron. Pinch ends of center fold and then cupboard fold. Crease and open mountain and valley folds as shown. Reverse fold corners. Open gently, turn over, and orient like the finished unit. Collapse center like waterbomb base. Continue assembling in a dodecahedral manner to complete model. Although traditional origami begins with a square, many modern models use rectangles.

The following is organized in ascending order of aspect ratio. Obtain paper sizes as below, and use them as templates to cut papers for your actual units. While many models look nice made with a single color, there are many other models that look astounding with the use of multiple colors.

Sometimes random coloring works, but symmetry lovers would definitely prefer a homogenous color tiling. Determining a solution such that no two units of the same color are adjacent to each other is quite a pleasantly challenging puzzle.

For those who do not have the time or patience, or do not Three-color tiling of an octahedron Every face has three distinct colors. Three-color tiling of an icosahedron Every face has three distinct colors.

In the following figures each edge of a polyhedron represents one unit, dashed edges are invisible from the point of view. It is obvious that for a homogeneous color tiling the number of colors you choose should be a sub-multiple or factor of the number of edges or units in your model.

For example, for a unit model, you can use three, five, six or ten colors. Four-color tiling of an octahedron Every vertex has four distinct colors, and every face has three distinct colors. Three-color tiling of a dodecahedron Every vertex has three distinct colors. Six-color tiling of an icosahedron Every vertex has five distinct colors, and every face has three distinct colors.

Six-color tiling of a dodecahedron Every face has five distinct colors, and every vertex has three distinct colors. Hence, it is not surprising that so many mathematicians, scientists, and engineers have shown a keen interest in this field—some have even taken a break from their regular careers to delve deep into the depths of exploring the connection between origami and mathematics. So strong is the bond that a separate international origami conference, Origami Science, Math, and Education OSME has been dedicated to its cause since Professor Kazuo Haga of University of Tsukuba, Japan, rightly proposed the term origamics in to refer to this genre of origami that is heavily related to science and mathematics.

It's a great book for all those origami creators One person found this helpful. Meenakshi has done a great job of explaining in a step-by-step manner how to create many simple to not-so-simple figures in Origami. Being a complete beginner, it has greatly helped me.

I am sure the more advanced users will get much more from this book.

This is the second book of the same author that I bought. It is a deception. The printing quality is very bad, the format of the book is not useful and the most important thing: The diagrams are not well done and the explanation is not clear. In general most of the model are adptation from others model but not very clear.

Truly is a very bad book! I got this book after browsing through the author's well-known website for modular origami. It's a very nice book explaining how to make great looking modular balls. The diagrams are very clear and well described with pictures showing how the modular unit should look like in each step. Being just over an year old in the origami world, I got stumped a couple of times but seeing the diagram of the next step helped me figure out the fold.

All I needed was a little bit of practice and a bit more patience. For beginners like me, it's a good practice to make one unit using a printer paper and understand all the steps. Also, I recommend reading the 'Homogeneous Color Tiling' section of the book if one is using multiple colors for making a model. I believe even a beginner, after getting a bit familiar with the basic origami diagrams, can fold the models in the book as there are no complex folds involved.

I highly recommend this book. And if you are into polyhedra and floral models, it is a must. This book has a lot of stuff in it and it will keep you busy for many hours, days, and weeks!

There are six sections in this book, each section contains models that are very similar to one another. They are grouped by their similarities. So, one could argue that there are not a lot of different models in this book; however, those who are familiar with modular origami will find that this is not so strange.

Indeed, a spiky ball with 36 points is not that different than a spiky ball with 48 points. The strength in this book is the demonstration of how small changes can evoke dramatic differences in appearance of the final model. If anything, I think this book teaches you how to experiment with your own variations-on-the-theme designs. Recommended for those who love modular origami.

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Marvelous Modular Origami

Amazon Drive Cloud storage from Amazon. These interests date all the way back to the late nineteenth century when Tandalam Sundara Row of India wrote the book Geometric Exercises in Paper Folding in He used novel methods to teach concepts in Euclidean geometry simply by using scraps of paper and a penknife. The geometric results were so easily attainable that the book became very attractive to teachers as well as students and is still in print to this day.

It also inspired quite a few mathematicians to investigate the geometry of paper folding. Around the s, Italian mathematician Margherita Beloch found out that origami can do more than straightedge-and-compass geometric constructions and discovered something similar to one of the Huzita-Hatori Axioms explained next. All geometric origami constructions involving single-fold steps that can be serialized can be performed using some or all of these seven axioms.

Together known as the Huzita-Hatori Axioms, they are listed below: While a lot of studies relating origami to mathematics were going on, nobody actually formalized any of them into axioms or theorems until when Japanese mathematician Humiaki Huzita and Italian mathematician Benedetto Scimemi laid out a list of six axioms to define the algebra and geometry of origami. Later, in , origami enthusiast Hatori Koshiro added a seventh axiom. Physicist, engineer, and leading origami artist Dr.

Robert Lang has proved that these seven axioms are complete, i. Given two lines L1 and L2, a line can be folded placing L1 onto L2. Given two points P1 and P2, a line can be folded placing P1 onto P2. Given two points P1 and P2, a line can be folded passing through both P1 and P2. Given a point P and a line L, a line can be folded passing through P and perpendicular to L. This can be demonstrated by geometry students playing around with some paper.

Discoveries similar to the Kawasaki Theorem have also been made independently by mathematician Jacques Justin. Physicist Jun Maekawa discovered another fundamental origami theorem. It states that the difference between the number of mountain creases M and the number of valley creases V surrounding a vertex in the crease pattern of a flat origami is always 2. There are some more fundamental laws and theorems of mathematical origami, including the laws of layer ordering by Jacques Justin, which we will not enumerated here.

Other notable contributions to the foundations of mathematical origami have been made by Thomas Hull, Shuji Fujimoto, K. Husimi, M. The use of computational mathematics in the design of origami models has been in practice for many years now.

Some of the first known algorithms for such designs were developed by computer scientists Ron Resch and David Huffman in the sixties and seventies. In more recent years Jun Maekawa, Toshiyuki Meguro, Fumiaki Kawahata, and Robert Lang have done extensive work in this area and took it to a new level by developing computer algorithms to design very complex origami models.

Particularly notable is Dr. Due to the fact that paper is an inexpensive and readily available resource, origami has become extremely useful for the purposes of modeling and experimenting. There are a large number of educators who are using origami to teach various concepts in a classroom.

Origami is already being used to model polyhedra in mathematics classes, viruses in biology classes, molecular structures in chemistry classes, geodesic domes in architecture classes, DNA in genetics classes, and crystals in crystallography classes.Origami 4 Origami AK Peters. Mountain fold along edge of back flap. Three-color tiling of a dodecahedron Every vertex has three distinct colors. First of all, I would like to thank my uncle Bireshwar Mukhopadhyay for introducing me to origami as a child and buying me those Robert Harbin books.

This would be an excellent reference for members of a mathematics club who are looking for projects. Fold and open corners, then valley fold preexisting crease. Lock two units together by tucking back along crease made in Step 5. Valley fold into thirds and open. Complete model by forming a total of 20 pyramids arranged in an icosahedral symmetry. She rediscovered origami in its modular form as an adult, quite by chance in , when she was living in Pittsburgh, PA.

DAINE from Kaneohe
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