Paper Pyramid Possibilities

 

When I was in college my roommate and I liked to fold origami. One day, while working with the traditional German Bell fold, we tried to combine several units (50 or so!) to form a bigger sculpture. Even though we achieved the feat of making a large sculpture, we thought, “If only we could figure out a way to make the sides straight, we could construct even more shapes with sturdy sides.” Well, after fooling around a bit we discovered that if we only folded the point of each corner to the bottom of the side, we could make straight sided pyramids. Wow! What a difference it made!

Interesting History:  While traveling with a quartet singing group in college we traveled to many states. While traveling in a Dodge van I folded many sculptures and gave them away at the stops along the way. Two years after I gave away one project I found it in a glass hutch still on display when I returned to the area on another trip. I also often used the rocket and satellite folds in a devotional at campfires and chapels. They were used to illustrate the need for taking the message of the Gospel to all the world just like the satellites are constantly communicating messages below.

 

After many years of perfecting the folds and finding new ways to combine them I thought it would be fun to share some of these with you. What kinds of things can you make using these pyramid units?

It All Starts With A Square:

To begin the fold you need a square of paper. Fold an X on one side, then turn it over and fold a cross. This gives you the lines to mark the folding pattern.

Next, you turn the paper in the diamond pattern. then fold an airplane point on the end like this:

 

Next, you fold the pointed end back down to the intersection of the cross shape below:

 

Fold Backs Are Important!

Repeat this on all four corners of the diamond. Don’t forget to fold the pointed ends back down on each corner. It may even look like it is already folded on one side, but it is not on the other. To check to see if you did it correctly, just look in the center of the diamond and you should see a square in the center. If one side of the square is missing, that is the point that needs to be folded back to the middle.

This Will Do In A Pinch!

Pinch in the middle of each side and you should see the star shape above. Next, you will lift the four points up to form the pyramid.

 

Part of the trick is when you glue it together. Before you glue the sides up, put a little glue inside two opposite sides and press down. This will keep the form from bulging out in the middle and makes it much easier to glue up the side pieces. (Hint: Do not do this when making the Gluck Interlock!)

 

Gluing Secret To Making A Sharp Looking Form:

Next, you will apply glue to outside edges of the pointed sides so they make contact with the upright middle points to form the pyramid. Be sure to put the glue only on the edges since the middle part does not make contact when the sides are raised. Just a thin line of glue will work. Too much will only take longer to set and will ooze out and ruin your forms appearance.

Many Ways To Combine The Base Units:

Now that you have learned how to fold and glue them into pyramids, lets see some other ways to combine them to make interesting shapes.

You can just start gluing them together on the sides. Here is what that looks like:

Discovering New Ways To Combine The Pyramids:

Through the years my students and I have found many ways to combine the units. Here are a few of the notable ones:

The Gluck Interlock: Take one unglued form and place it upside down on top of another unit. Glue in place. This base form gives you many places to glue additional units.

If you start with one Gluck Interlock and place a pyramid on every surface you will construct a neat satellite like the one on the right below:

 

If you stack five Gluck Interlocks on top of one another then add a nose cone and fins, you get the rocket on the left above. Using hole punches you can decorate the sides to make a more interesting sculpture.

Experiment and you may discover other ways to combine them to make many interesting projects. One of the most amazing is the Globe Base seen at the middle of this sculpture:

In the above sculpture I added pyramids to the six end pieces to make this form.

One of my students was trying to make a Gluck Interlock and stumbled upon a new interlock. This is the Voiles Interlock: It looks like a crystal and allows you to make long straight columns:

Another student glued seven of the pyramids into a circle to make the Keifer Interlock: You can see the wheel base in the center of this star form to which I added seven outer pyramids:

        Star Attraction:

What If You Start With A Triangle?:

If you start with a triangle, instead of a square, you can make long, slender triangular pyramids. They can also be combined to make many interesting form. Here you can see some insect legs combining several units:

By combining these forms together the possibilities are endless. I have had students construct many different animals, buildings, aircraft, vehicles, and more. One student even made a robot from Star Wars.

This was one I made to hang in my classroom. We called it the Revolving Rooster.

See what can be made from triangle units below. These were made with recycled computer paper from the days when the paper had holes along the sides to be pulled through the printer on sprockets.

Now It’s Your Turn!:

So…..The Question Is……What can you make?

The Five Dollar Star

 

 

The Buck Stops Here!

One of the most interesting categories of origami includes those folds that can be made from dollar bills. As you probably already know, the majority of origami folds begin with a square, although many different shapes of paper may be used. In this case, a dollar, is a rectangle that is two squares connected in the middle.

I found this fold while exploring folds that begin with rectangles. If you are doing this for the first time, or do not have extra cash hanging around, you can just start with rectangular pieces of copy paper.

 

Why Not Recycle?

I happen to have a stack of old papers printed on one side. I decided to turn this scrap paper into some beautiful stars. You can use practically any type of paper as long as it holds a crease and isn’t to brittle so that it doesn’t tear too easily.

 

Let’s Make a Star!:

 

Begin with your rectangles. You will need at least five pieces, though you can also make six pointed stars. Fold a line right down the middle of the rectangle to use as a target for the following folds.  Next, fold an airplane fold on each end that make the two ends pointed.

Now fold one end up just under the point on the other end. Flip the paper over and unfold the point on the end that is still pointed.

 

Next, fold an additional airplane point on top of the previous one to make the point even thinner.

 

 

Now that that you have a point like the picture above, flip the paper over so it looks like the one on the left below:

Fold and Tuck:

The next thing to do is to fold the bottom edge up under the flap and make a crease so it stays in place when tucked under the top flap. Next, fold it again and tuck, and then the third time. This will make the extensions needed to hold the form together.

Open Wide….It Will Be Easier!:

Turn the units over so you can see the little pockets on the back of the paper. Open these with a pencil so it will be easier to insert the tabs. Take another unit and insert the tab into the small pocket on one side of the paper. Then flip the whole thing over and insert the other tab into the big central pocket on that side. I found it easiest if you do the small pockets before the big ones. It takes a little while to get the tab inside the big pocket. Curl the end before inserting it and it is easier.

Paper Is Flexible….You Need to Be Flexible Too!

 

If this is your first time folding these units, don’t get too frustrated. It is a little difficult to get the tabs in place, especially the ones on the front side. The paper, however, will slip into the pocket if you don’t give up. It is like a foot going into a tight shoe with a shoehorn.

 

It Needs Five or Six Points:

After inserting all the tabs on five (or six) units you will have a star. You can adjust the angles a bit by pulling on the points if the star is out of alignment.  Your finished forms should look something like this:

 

Feel Free To Decorate Further (Unless you made them with dollars!):

If made of paper the stars are easy to decorate. You can spray paint them a metallic color. You can add dots made by punching colored paper with a hole punch. You can use crayons, colored pencils and pens to add designed. If you add a string, they make neat mobiles and Christmas Tree ornaments.

 

 

Fabricating Fabulous Forms For Fun

 

Combining Units 

One of my favorite varieties of origami is Unit Origami. In this art form you combine several modular pieces to create a larger form. Using the same base you can make several different models. Here are a few of the forms I made with the same base unit. You can also make larger and smaller objects by varying the size of the squares of paper you begin folding. By adding dots made with a hold punch you can add color and texture to your piece. There are several ways to modify the designs by changing the colors of the dots as well as the placement. One of the reasons I like this unit is that it requires no glue to hold the original form together. I did use glue to attach the dots.

 

I See Spots!

 

Let’s Make Some Dice!

If you add spots, you can make your own set of dice.

What Can You Make With 12 Units?

Here is a geometric form composed of 12 units. It is about the size of a baseball if you make it with squares that are created by quartering a sheet of copy paper. Of course, you will have a small strip of paper left over after folding the paper in quarters and folding it diagonally to make squares. Did you notice that the dice above were made with smaller units than the globes? These were made with squares cut from the strips leftover from the globe construction.

 

One of My Favorite Origami Books

There are actually more than one way to create the units used in these forms. The units I used in all the previous projects are a variation of one I found in Steve and Magumi Biddle’s book, Essential Origami.   You can find the directions for folding the units on pages 173-176 of their book. To make an easier unit, but with less color, just roll the paper to the center twice instead of going beyond the center and reverse rolling. Below you can see a cube made with the Biddle units and an example of the units used to compose the cube next to a modified unit of the same size.

Below is a picture of one of my favorite origami books.

How Would You Use Them?

By experimenting with this unit you can find others ways to combine them. They can be used in a wide variety of ways including: making your own indoor baseballs to play catch, using several combined forms to create mobiles, using forms as knick-knacks and conversation pieces, making your own playing dice for game play, and more. Fill one of the small cubes with beans or rice and you have a Hackensack, You can also use the small globes as Christmas tree decorations. How could you use them?

 

How to Make an Origami Four-Leaf Clover

In one of my previous posts I shared with you about the four-leaf clover. It’s not luck. It’s God’s providence. Even though the four-leaf clover can not bring you good luck, it can remind us of its Creator and how our relationship with Him is different from that of the world apart from Him. Each year, on St. Patrick’s Day, we see a lot of these clovers. Interestingly it is said that St. Patrick often used a the more common three-leaf clover to remind others of the Holy Trinity: Father, Son, and Holy Spirit.

If you want to fold a four-leaf clover, follow these steps. It makes a fun ornament for St. Patrick’s Day.

 

Begin with a square of green paper. It doesn’t matter the size, just that it is square. Fold an X on one side of the paper and then turn it over and fold a cross on the middle. Now, turn it over and it should look like this:

 

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Next, fold the four corners to the center. This is called a Blintz fold.

Next, turn the paper over and fold the four corners to the center again.

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And next, yes, turn it over and Blintz the paper again. It should look like this:

 

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Now we we need to form the leaves. On the way we will form a cross shape.  To do this we need to pop out the four corners and squash them flat.

 

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Repeat this on all corners until you have a cross.

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Now we we need to shape the leaves by crimping the edges of each side of the cross.

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Now we need to pocket-fold these beveled corners inside the piece.

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When completed it looks like this:

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You can make it more 3-D by valley folding the middle cross shape and the squeezing the outside. This makes it hold its shape better.

Now all you need is a stem. This is the easiest part! Just cut a piece of paper into a rectangle and the fold it in half length-wise two times.

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Finally, turn the top of the clover over and insert the stem into one of the pockets on the back of the clover.

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And there you have it…a four-leaf clover! Make up a bunch and use them as party favors for your St. Patrick’s Day celebration.

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How Flexible Is Paper?

In my last origami post I showed you the weight bearing strength of paper. In this post I want to show you a fun fold I learned way back in my college days. This amazing fold creates a 3-D form that rotates on its axis. It is called a Hexaflexagon.

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The first time I made one of these it took hours to complete because the directions  required you measure out the form, then line it for all the folds. After that, you had to score all the lines with a sharp knife. Only then could you fold it, squash it, and finally glue it together. After making several flexagrams the hard way, it dawned on me that it was simply a repeating pattern. Why not just fold it Origami style, since all the lines were straight? It’s just a series of diagonal and horizontal folds. I tried it and can now make one very quickly, with any sized paper, as long as it is just over three times its width, allowing for the glue tabs.

 

This is a rather complicated project the first time you do it. It usually takes two whole periods to teach junior high and high school students how to fold them. It’s much easier when someone is there showing you how in person. The following just tells you the basic steps of the process.

 

You  begin by folding the paper diagonally to create the three original squares which form at the ends of the X folds. After that you divide each square into four horizontal folds. Next,  you must fold the four corners of each square to the center of each square. At this time you can see the pattern all made up of triangles. You just need to find where the pattern is missing in your project  and add the missing folds. Once this pattern is completed you will need to crease all of the horizontals into valley folds. Next, turn the paper over and fold all the diagonals with valley folds. The paper will start to curl up when you do this. Grab one end of the fold and squeeze the outside of the form, where you see little triangles, to the center with your fingers while compressing the form. Continue all the way to the end of the form until you have a tiny square, springlike form. Open it back up and cut the extra band of paper into the glue tabs. Add glue to the top of the glue tabs and insert them into the inside of the form one at a time. Squeeze it for about a minute to allow the glue to set. Rotate the form so that you can insert the second glue tab. Again hold it for a minute or so.

 

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You have now made a hexaflexagram. To make it rotate you must pull on the outer edges while pressing the center in. It will rotate one facet at a time. Be sure to always keep the center tightly together as you rotate it or the glue tabs may fail. After you have tried rotating it a couple times it will be easier.

Some people think this form is a good model of a black hole. One that takes you through its center to another dimension. Others liken it to a flying saucer, complete with landing gear. The saucer closes up to travel through space yet can rotate to open its landing gear.

 

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If you make multiple units they stack and interlock like gears. Stack four on top of each other and bind together with rubber bands and you have a great indoor football to throw. I wouldn’t try kicking it though. It would probably break depending on how hard you kicked it.

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Another fun way to use them is to create  3D greeting cards by adding art to the surfaces. You can even make a progressive message that appears each time you rotate  a new surface.  I once won a contest with my Christmas card design created on the hexaflexagram base.

 

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Interestingly, there are several other types of flexagrams. If you are interested in these, check out the M. C. Escher kaleidocycles. They flexagrams come in book form with cutout models. They are printed with Escher tessellations on the outside which make wonderful conversation and art pieces.

As you have seen in these pictures, the Hexaflexagram is amazingly flexible. It is also strong enough to support weight, much like the accordion pleat in the last post. I hope you have enjoyed learning about flexagrams.

Origami Lifting Power

I recently watched an amazing documentary on Nova about the engineering developments using the principles of origami folding. They gave examples in building designs, medicine, mechanics, aeronautics, architecture, outer space design, and so much more. As a hobby I have experimented with the power of a piece of paper in its weight bearing abilities. I thought you would enjoy seeing one example.

 

In this example I used two standard 3″x5″ cards folded with accordion pleats. How many books do you think one card can hold up?

 

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Notice I placed two smaller books on the sides to prevent the paper from sliding outward. The cards still support the entire weight of the books.

 

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You can see that the larger books are resting on the cards and not the smaller books.

 

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In total, the cards were able to support the weight of seven large books. When weighed, that equals 10 lbs. Who would have thought a tiny 3″x5″ card could support so much weight?

 

When used in weight bearing applications the paper is sandwiched between an outer frame that keeps the sides from slipping out yet still allowing the internal paper to support the weight.

Keep your ears and eyes open to hear and see many of these origami principles being used in the news. More and more people are realizing that origami is not just a kid’s hobby. Did you know that many of the most famous scientists experimented with origami? Other notables were famous authors, musicians, magicians, doctors, architects, and more. Why not do a little research about the history of origami? It is very interesting.

Origami Bookmarks

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Some Origami folds can be very useful. One of these is the triangle unit from which you can construct bookmarks.

Here are a couple of the ones I have made from this unit. If you glue two together you can make a Star of David. Using smaller units glued to larger units, you can make any number of patterns.

The triangle fold begins with a triangle. You fold the three points of the triangle to the top middle above. Next, you fold the top layer point down to the right corner and crease it. Do this on all three corners. Next, you lock these three tabs together like you would a cardboard box. Each of the three sides has a pocket which will slip over the corner of a book page to mark your spot.

 

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Unit Origami Forms

  • These are a couple unit Origami folds that I have folded from models in books. The largest is composed of 30 units, all folded the in the same manner. These units can be combined into other forms like a 60 unit module. The two smaller spheres are made with different units. Each of these has 12 units. Using the same units you can make a variety of shapes. Using 6 units you can make a box. Many other forms are possible. This particular unit is one of the most sturdy units for construction. When you push on the outside of the spheres, once combined, they tighten almost like when you press on the outside of a snow ball. They hold together so tightly that you can play catch with them. The other units usually need a tiny dab of glue to keep them together for a more permanent display. There are many different units you can fold to make a wide variety of forms. Why not check out some of the unit Origami books at your library and give it a try?
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Have you entered into the Treasures of the snow?

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How many of you have a favorite Christmas ornament? Think of how it looks and what it represents. I have several ornaments that mean a lot to me. Some of them are special because of who gave them to me. Others are favorites becuase of what they represent or how unique they are in design. Some are neat because of the materials used in the construction of the ornament.

Today, I am going to make an origami Christmas ornament. It is actually modeled after an ornament the Lord Jesus designed when He created the world and everything in it. This model is one I designed after the better design of Jesus. It not only is fun because it is made out of ordinary white paper, but also because of what it represents.  It’s pattern is neat, also.

Watch as I fold this project. I’m going to read several Scripture passages, which talk about this ornament as I work. Listen carefully so that you can share the message of God’s Word with others this Christmas time.

Way back in the Old Testament, a man named Job was talking with God, when God asked him a question. It is a very interesting question. Before I read you the question God asked him, we need to know a little bit about the circumstances Job was in when God talked with him. Job, as you probably know, had more problems than anyone else in the Bible. He lost all his wealth, his children, and his health all in the matter of a few days. He actually was under the direct attack of Satan when this happened. On top of these problems, Job’s friends tried to tell him that all his problems were because he was not right with God. What a terrible place to be in!

Well, after all this hard stuff happened, God came to Job and wanted him to know He was still in charge, that He loved Job, and knew his problems and could fix them. He then asked Job this question: “Job… Have you ever entered into the treasures (storehouses) of the snow..?” (Job 38:22). That seems like a funny question to ask him at that time, doesn’t it? But God knew what He was talking about. The storehouse of the snow is composed of what? Yes, snowflakes. I’m making a snowflake ornament.

What are some of the things we can learn about God from the snowflakes He created? First, we notice that almost every single snowflake is different yet it follows a similar pattern. God takes great care in the forming of every snowflake. Each one shows His power and majesty. It also shows us that God cares about little details and little things as well as the big things.

We can also look at what the Bible says about snow. Did you know It uses snow as a picture of God’s cleansing from sin? Listen to this neat verse from Isaiah 1:18: “‘Come now, let us reason together,’ says the Lord. ‘Though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool.’”

Wow, just think of the color red! It stands out like a sore thumb and screams, “Look at me!” Our sins do the same thing. They show us and everybody else that we are not good enough to meet God’s standard of perfection, holiness, and purity. We can’t make it on our own. We need our sin to be removed in order for us to be able to come into the presence of a holy God. Jesus’ blood, RED, was shed to cover our sins, to pay the price, to remove our sins. We are pure (WHITE) because of His sacrifice.

If you look carefully at a snowflake, under a microscope, you would find a piece of dirt or dust in the center of every snowflake. It is called a “condensation nuclei.” While the dust or smoke particle is floating around in the air, the water vapor up there collects on it and than the cold air freezes around the dust particle and completely hides it. The result is a beautiful snowflake design. The snowflake falls and the dirt particle is removed from the air. The snow falls on the ground and covers everything to make it look so beautiful and pure.

Remember King David in the Old Testament? He also wrote about snow. He said this to God in one of his prayers, “…Now wash me and I shall be whiter than snow…” (Psalm 51:7b).

He wasn’t asking God to throw him into the bathtub. He was confessing his sin and he know that only God could cleanse his heart. We also can have our hearts clean when we do the same thing. First John 1:9 says, “If we confess our sins, He is faithful to forgive us our sins and cleanse us from all unrighteousness.”

If you are feeling dirty because of the wrong things you have done, ask God to forgive you. Tell Him what you did wrong and agree with Him that it is wrong. Turn from it and He will forgive you and cleanse you. Wow, that’s neat. It’s just like waking up in the morning and finding the ground covered with pure, white snow. We are all clean and fresh.

Snow is neat in many other ways. As you know, it’s fun to play in, ski on, ride sleds over, and it provides us with a way to store the water until we need it in the spring and summer. We should thank God every time we see the snow for His grace and mercy and the blessings we have because of His creation.

The next time you see a snow scene, and I’m sure you will see many over the Christmas holidays, think about your life and how God has cleaned you up and made you pure so that you can fellowship with Him and go to Heaven in the future. If you take the time to think about it and study about the snow, I bet you can find out many other amazing things about these little jewels of ice.