Origami tessellations pdf

Christmas trees are possible. Weed control is an important cultural practice in Christmas tree production throughout the year. You will get Christmas tree templates PDF today if your little one is looking to paste one on his special home-made Christmas card. Christmas Trees can also be in the form of attractive and unique color painting on high-quality pieces of.

Color the pattern and then work out how to tesselate the gingerbread houses for a fun and easy Christmas Math activity. This could more than a whole lesson if you get the students to tessellate a design and then also colour it great for displays.

Use the Christmas trees for your own crafts and Christmas activities. It connects the individual with the group using tessellations and it has a ton of wow factor when complete. To cut Christmas trees.

Christmas themed tessellation activity for students to complete in class or for homework. You should find 3 regular tessellations. Color the pattern and then work out how to tessellate the Christmas tree for a fun and easy Christmas Math activity. You may also like. Skip to content Are they the same shape. Tags christmas tessellation tree. Count down five grid squares from the edge of each tile and identify a new square. Fold the two facing pleat intersections first for each of the new squares see photo 4.

Then, fold the outer two pleat intersections to complete each new square tile see photo 5. Depending on the type of paper you use, your finished piece might curl a bit. To fix the problem, place your folded tessellation between the pages of a large, heavy book.

Be sure all the creases and pleats are lying exactly how you want them, be- cause the pressure of the closed book will make the creases permanent.

Leave your tessellation in the book overnight. By morning, you will have a nicely pressed origami tessellation! Til' Accuracy is the key to folding origami tessellations. A lack of precision can derail any project.

Remember: Good work going In means good work coming out! This design was the first origami tessellation I discovered on my own. Sixteen divisions will help you understand the idea- and it's a good place to start-but 32 divisions will show off the design to its fullest. Locate the center of the grid, and mark out a hexa- gon that's two triangle lengths to a side. The resulting hexagon will be four pleats across in all directions. The result- ing hexagonal tile in the center of the paper will have pleats radiating out from each corner see photo 1.

Start counting at the base of the hexagon. Because one pleat length is underneath the hexagonal tile, it will look like you moved only one pleat away see photo 2. Fold another degree pleat intersec- tion here, making sure to fold the new pleats away from the center.

This new pleat intersection is actually the edge of another hexagon tile. As the new pleats intersect each other farther out on the paper, just fold them over one another-this arrangement is only temporary. When you have completed all six degree pleat intersections, you will see a star-shaped design with the hexagonal tile in the center see photo 3.

Make two new degree pleat intersections where the tip of the star is two grid triangles wide. This action creates a new hexagon tile, identical in size to the central hexagon and seemingly positioned underneath it. Work around the star, creating five more hexagon tiles see photo 4. Count two pleats outward, fold a degree pleat intersection, and repeat. Fold the overlapping pleat intersections to make a new layer of hexagonal tiles see photo 5. Each layer has more and more hexa- gons as you work your way outward.

By maintaining the same pleat orienta- tion, the folds will all flow into each other. You can continue this tessel- lation into infinity by following the basic folding pattern. See an extended version of Spread Hexagons on page in the Gallery section. Fold the next corner in the same manner, except in the opposite direction: If you folded the first pleat in a clockwise direction, fold the second counterclockwise.

Continue around the hexagon following this pattern see photo 1. These folds form the base for the rest of your work. The entire pattern flows from them. This move raises up the degree pleat intersection.

Now, squash it flat into a triangle twist see photo 2. Re- peat the squashing all the way around the central hexagon see photo 3. In this design, every pleat intersection should twist, and every twist should be a triangle. Work your way around to create a new hexa- gon with triangle twists. The new hexagon will share two triangles with the center hexagon see photo 4. The pattern can continue on to the edge of your paper. The design is easy to fold and provides a great introduction to the often-curious properties of triangle twists.

Continue outward from the central hexagon, folding triangle twists at every corner of each adjoining hexagon see photo 2. Proceed in orderly fashion, folding every corner of a given hexagon before moving to the next hexagon. The six twists are composed of three flaps, each with two connected triangle twists.

Open these flaps see photo 3 to create a triangle with three pleats on every side. S Push up on the triangle from the opposite side of the paper to pop up a bubble hexagon. Continue to push up from below with one hand while you push in the sides of the hexagon with your other hand to create star points see photo 4. The sides should simply pop into place as you create a three-dimensional six-sided star.

You can create many variations by popping different arrangements within the pattern. Be sure to wash your hands before every folding session. Hand oils and acids corrode paper. Dirt and grime never make for good origami! Star Puff 39 I I beginner projects o 3. First discovered by renowned origamist Shuzo Fujimoto, 3. These twists fold properly in only one direction! Remember that one pleat is hidden under the hexagon, so you will see only two pleats between the edge of the hexagon and the new pleat intersection.

Continue around the pleats extending from the hexagon twist, folding five more degree intersections. You'll notice an odd bunching of pleats farther out now that you have folded a triangle twist. This pleat intersection is actually another hexagon twist. It just needs to be roughed out and brought into shape see photo 3.

You'll notice more pleats that do not lie flat and that connect the hexagon twists together. They are triangle twists waiting to be squashed flat see photo 4. Oblige them! As with all tessellations, this pattern tiles in- finitely, so once you get the hang of how the basic pattern of hexagon twists and triangle twists comes together, you can extend it out as far as you'd like.

Deglnner proJecrs My trial-and-error experiments folding pinwheel shapes yielded this wonderful tessellated pattern. Easily among my favorite designs, I hope it becomes one of yours, as well.

Precrease the outlines for one of the triangles shown in the crease pattern. See photo 1: The triangle is set to the right of the hexagon. This triangle will form an open-back triangle twist. Collapse the open- back triangle twist, which will fold flat quite easily along the crease lines. You'll encounter some trouble- some pleats that intersect between the two triangle twists.

These pleats eventually will become another hexagon twist, but for now fold them flat using the techniques detailed in the degree pleat intersection instructions on page Rather than folding the pleats toward each other, fold both over in the same direction see photo 2.

Although you can leave the pleats loose, you'll be folding them into hexagon twists shortly, so it's best to lay some of the groundwork ahead of time. You've already folded two of the six corners! At one of the unfolded corners, form a degree pleat intersection-refer to the crease pattern for location guid- ance, if you need help.

Repeat the step on an adjacent hexagon-twist-to-be, and form an open-back triangle twist between the two see photo 4.

Again, use the crease pattern as your guide. S Work your way around the hexagon twist being formed, creating pleats and folding open-back triangle twists. When you're finished, make sure the twists are fully flat.

You might occasionally need to unfold one a bit and twist it in the opposite direction for it to fold completely. A good fold makes a nice, clean twist closure on the reverse side of the paper. Pinwheel 45 46 Pinwheel ill' Crease heavy paper with a bone folder, like the one pictured here, or another hard, smooth object. Save your fingers and fingertips for more delicate folds. Even though the underlying patterns are similar between the two tessellations, a slight modification to Open-Back Hexagon Twist dramatically alters the final piece.

Once you complete the design, your biggest question will be which spectacular side to display. Count outward three pleats along the pleat line extending from one corner of the open-back hex twist, and fold a triangle twist centered on the third pleat see photo 1. You'll notice the pleats extending from the triangle twists interfere with one another. Where they intersect, fold another open-back hexagon twist. This new open-back hex twist will connect the two pleats, pinching into place an offset line from a point two pleats away from the tip of each triangle twist see photo 2.

Move to the next radiating pleat, and make another triangle twist. Create another open-back hex twist, and fold an additional triangle twist between the two secondary open- back hex twists where their radiating pleats intersect see photo 3. Continue working around the central hexagon, fold- ing triangle twists and open-back hexagon twists. The tessellation takes on a natural curve and dimensionality during folding.

The final piece resembles a woven basket made of rattan. A common design, I was first introduced to this pattern by Joel Cooper. Think ahead! Consider how wide your final pleats will be.

A little planning will prevent a lot of Instructions 1 Start with a triangle grid, and fold an open-back hexagon twist in the center. The triangle twist will overlap the initial hexagon twist. Repeat this process for all sides of the hexagon. Fold open-backed hexagon twists where the pleats from the triangle twists come together. See photo 3, which isolates folds on one side of the hexagon, and photo 4, which illustrates how to "tuck under" these folds.

Look at this side to verify the accuracy of your work. You should not see any double-wide pleats or other shapes-only hexagons and thin strips of single-width pleats that all line up cleanly. Try experimenting to discover which layering scheme you like best.

By tiling a simple base with squares, you achieve a three-dimensional surface that's both pliant and curving. The larger you scale the pattern, the more the surface of the paper curves.

After a certain point, the remaining folds will pop into place almost on their own. S Lay the tessellation down on a flat surface.

The ten- sion of the paper forces the pattern apart, which causes it to curve, particularly toward the corners. Hold the paper down at the corners and push the pattern together. Pinch the vertical folds tightly, one by one, to reinforce the precreased folds and to give the paper some "memory" see photo 3.

A Water Bomb tes- sellation clipped to hold its shape overnight will remember that shape for a very long time! See an extended version of the Water Bomb tessellation on page in the Gallery section. The Square Weave project is a terrific introduction to offset square twists. The finished model is attractive on both sides, featuring a woven pattern on the front and sets of square twists on the back that appear to shimmy across the paper.

Please note: Dollar bills folded into square weaves make popular tips at restaurants! This size grid allows the square weave to perfectly fit three open-back square twists across the paper. Using a square grid of 32 divisions will give you enough room for six open-back, or offset, square twists across the paper.

Use the crease pattern for reference if you' re not sure exactly where to place the first twist. If you folded the first one with a clockwise tilt as in photo 1 , fold the second twist counterclockwise. Follow the pleat running to the right from your central twist, and count outward two grid squares.

Locate the second square twist so you have two pleat spaces between the respective squares' corners see photo 2. Repeat step 3, folding another square twist. You now have three offset square twiSts, lined up across the center of the paper see photo 3. Utilize this understanding in placing the next three twists on the top third of the paper see photo 4.

Choose a translucent or light paper, because a beautiful pattern appears when the piece is backlit. This tessellation has quite a few diagonal creases, and working the piece will be much easier if you fold them ahead of time rather than as you go along.

Make sure the valley- and mountain-fold orientations are correct, because the design won't fold together properly otherwise see photo 1. II 2 Choose one of the piece's corners and start collapsing the design together along the crease lines see photo 2. Don't worry about folding every- thing completely flat at first.

Rough the folds into shape, which will allow more of the design to fall into place as you work your way around the edges see photo 3. When you're close to finishing, you can fold the paper a bit more tightly-you'll get less resistance from the paper. The octagon connection points between the main folded sections on the front will be standing out, resembling puffy X shapes see photo 4.

Fold these connection points flat by grabbing the edges and pushing the extra paper inward while pressing the paper flat. The paper should collapse relatively cleanly. Once flattened, each point will look like a small octagon lying on top of an X see photo 5. Work your way up to working with larger paper once you have a lot of practice folding smaller pieces. Unlike many of the projects in this book, where you start isn't critical. Because the entire design is made up of tiled rhombi, the pattern blends together.

This twist will point in a different direction from the first one. Rhombus twists in this design have only two orientations, and now you have folded both of them. The precreased rhombus points in the same direction as the rhombus you just folded, but when you twist it, the new rhombus reorients in a different direction. S After collapsing the newest twist, you'll notice the pattern essentially consists of a series of steps moving up and down across the paper.

Keep folding twists, follow- ing this simple pattern, until you have folded the full length of the paper see photo 3. However, these lines also make it much easier to see exactly where your new twists need to go. Think of the pleats as helpful guides rather than pesky intruders! New twists still follow the same rule: Crease lines for new rhombus twists point in the same direction as the previous twist.

Start another row, and move along sequentially for best results see photo 4. If you started with a square piece of paper, your finished tessella- tion will be in the shape of a rhombus. Curious, isn't it? Either way, its simplicity and symmetry trigger natural wonder. The pattern lends itself to easy modification, experimentation, and innovation. Instructions 1 Utilizing a triangle grid with divisions of 32 pleats or more, fold a hexagon twist at the center of your paper. Make sure the two outer pleats are facing away from the central hexagon twist see photo 1.

The easiest way to tile the basic star twist is to treat the degree intersection folds at the tips of the star as one third of a hexagon twist and fold two more star twists, all connecting at that central point.

Our final model for this post is something very unique. Ilan Garibi used origami tessellation techniques to make this paper QR code. The crazy thing is that this QR code actually works. If you hold your phone up to your monitor you can actually scan it! If you want to get into origami tessellations we recommend you check out the book Origami Tessellations: Awe-Inspiring Geometric Designs by Eric Gjerde.

Escher December 14, In Shapes. There are 2 major types of tessellations, the classic type and corrugations. This model uses 64 sheets of paper. Garibi started to create tessellations ten years ago and since then has designed more than unique models. This book is focused on square-grid based tessellations and presents some of his most unique models.

Roughly, an origami tessellation is a flat-folding of a piece of paper based on a tessellation or tiling of the plane [17]. One way to make this notion more precise [22, 35] is to consider the whole plane as the This new edition of Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design introduces an innovative pleat pattern technique for origami designs that is easily accessible to anyone who enjoys the geometry of paper.