Origami Double Spearhead Tessellation (Michał Kosmulski)

Origami Double Spearhead Tessellation (Michał Kosmulski)


Hey guys, this is Evan from EZ Origami! And today I’ll be teaching you how to fold an Origami Double Spearhead Tessellation designed by Michał Kosmulski. This model is not very difficult to fold, and it’s perfect for anyone who is interested in learning more about tessellations. So let’s start with the basics. Some of you may be wondering, what is a tessellation? And to put it simply, a tessellation is essentially a repeating pattern of identical shapes, which we’ll be referring to as molecules. So for the Double Spearhead Tessellation, a single molecule looks like this. And when several of those molecules are folded from a single square, they form a tessellation like this. In this video, I’ll be teaching you how to fold a 2 x 2 tessellation meaning that we’re going to fold 4 molecules from a single square. And throughout the video, I’ll also explain how to expand this tessellation in case you’d like to try folding more molecules from a single square. And this model requires 1 square sheet of paper. If this is your first time folding this model, I recommend using an 8 inch or larger square. Using an 8 inch square will result in a model about 4 inches wide. I’m going to be using paper with color on both sides, but if you’re using paper with color on one side and white on the other, then start with the white side up. And we’re going to start by folding in half vertically. So take this right edge and fold it over to the left edge Align the corners and the edges. Then make your crease. And then unfold. Then we’re going to rotate the paper 90 degrees, and we’re going to do the same thing. So once again, fold over this right edge and align it with the left edge. Align the corners and the edges, Then make your crease. And then unfold. And now we’re going to fold up this bottom edge, and align it with this center horizontal crease. So we’re just going to pull up the bottom edge like this. And once it’s completely aligned with that crease, then you can make your crease. And then unfold. Then we’re going to rotate the paper 90 degrees, and we’re going to do the same thing. So once again, we’re going to pull up this bottom edge. And once it’s aligned with that center horizontal crease, then you can make your crease. Then you can unfold. And then we’re going to repeat this process on the other two sides. So again, rotate the model, fold up the bottom edge, And once it’s aligned with that horizontal crease, then you can make your crease. And then you can unfold. Then we’re going to rotate the paper one last time, and again we’re going to pull up the bottom edge. Align it with that center horizontal crease, and then you can make your crease. And then you can unfold. And now you can see that we have a 4 x 4 grid. And with this grid, we’d be able to create 1 tessellation molecule. And what we’re going to do is sub-divide this grid even further. So we’re going to make an 8 x 8 grid. And with that, we’ll be able to fit 4 tessellation molecules within the same square. So in order to do that, we’re going to start by folding up this bottom edge, and aligning it with this bottom-most horizontal crease. So we’re just going to fold it up like this. And once the entire edge is aligned, then you can make your crease. Then you can unfold the flap that we just folded up, And you’ll see that we sub-divided this strip of paper here. So in order to divide this section, we’re going to fold up this bottom edge and align it with this top-most horizontal crease. So we’re simply going to pull it up like this. And once the bottom edge is aligned with that horizontal crease, then you can make your crease. Then you can unfold. And you’ll see that we’ve divided this section here. So now we’re going to rotate the paper 180 degrees, and we’re going to do the same thing. And once again, we’re going to pull up the bottom edge, and align it with the bottom-most horizontal crease. Just like this. Then you can make your crease. Then you can unfold the flap that we just folded up. And in order to divide this strip here, we’re going to fold up this bottom edge, and align it with this second horizontal crease from the top. So we’re just going to pull up the bottom edge like this, and once it’s aligned with that horizontal crease, then you can make your crease. And then you can unfold. And now you can see that we’ve divided the grid into eighths in this direction. So what we need to do is rotate the paper 90 degrees, and we’re going to do the same thing. So again, we’re going to start by pulling up this bottom edge and aligning it with the bottom-most horizontal crease. Then you can make your crease. Then unfold. Then we’re going to fold the bottom edge up to the top-most horizontal crease. So just pull it up like this, align it with that crease, And then you can make your crease. Then you can unfold. Then we’re going to rotate the paper 180 degrees. And again we’re going to fold up the bottom edge and align it with that bottom horizontal crease. Then you can make your crease. Then you can unfold. And to divide this last section here, we’re going to fold up the bottom edge and align it with the second horizontal crease from the top. So we’re simply going to pull it up like this. And once the bottom edge is aligned with that crease, then you can make your crease. Then you can unfold. And now you can see that we’ve created the 8 x 8 grid that we will need for the tessellation. So what we’re going to do is turn the paper over so that all of the creases are now mountain folds. And you can see that I’ve marked these 2 center creases. Because from this point on, I want you to think of this square as 4 separate squares. And each square represents its own separate molecule. So like I mentioned before, we need a 4 x 4 grid to fold a single molecule, which is why we’re using an 8 x 8 grid to fold a tessellation with 4 molecules. And for those of you who want to expand this tessellation beyond 4 molecules, you can see it would be easy enough to repeat this pattern on a larger starting grid. And now we’re going to continue with the pre-creasing. And as you will see, we’ll be creating the same creases within each of these 4 squares. So we’re going to start with this bottom right square here, And what we want to do is start in the bottom right corner, and we’re going to count the squares along this diagonal. So we’re going to count 1, 2, 3 squares. And what we want to do is fold this bottom right corner up to the top left corner of that third square. So we’re going to do that by lifting up the bottom right corner, And once it’s aligned with the top left corner of that third square, then we’re not going to crease all the way. You’ll notice that there are 3 triangles along this edge, but we only want to crease within this center triangle. So we’re just going to flatten out the model, and make a small crease within that center triangle there, and then you can unfold. And now we want to make a crease here. So what we’re going to do is count 5 squares from the bottom right corner, And we’re going to fold that corner up to the top left corner of this fifth square. So we’re just going to pull it up, just like we did before. And once the bottom left corner is aligned with that intersection, then again we’re not going to crease all the way. You’ll see that there are 5 triangles along this edge. But we only want to crease within this center triangle here. So we’re just going to carefully flatten out the model and make a crease within that center triangle. And then you can unfold. Then we’re going to rotate the paper 90 degrees. And we’re going to do the same thing on this bottom right square here. So again we’re going to fold the bottom right corner up to the third square. Then we’re going to make a small crease within that center triangle. And then you can unfold. Then we’re going to fold the same corner up to the fifth square this time. And once it’s aligned, then we’re just going to crease within that center triangle once again. Then you can unfold. And then we’re going to repeat this process on the remaining two squares. So simply rotate the model, and we’re going to do the same thing. So again, fold the bottom right corner up to that third square. Then we’re only going to crease within that center triangle. And then you can unfold. Then we’re going to fold the same corner up to the fifth square, just like we’ve been doing. Then you can make your crease. And then you can unfold. And now we’re going to rotate the model one last time. And we’re going to do the same thing. So again, fold the bottom right corner up to that third square. Then make your crease within that center triangle. And then unfold. Then we’re going to fold the same corner up to the fifth square. Once it’s aligned, then you can make your crease within that center triangle. And then you can unfold. And you can see that we’ve made those creases in all 4 squares. And now we’re going to count up 7 squares from the bottom right corner, So we’ll end up in this square here. And what we want to do is fold the bottom right corner up to the top left corner of that seventh square. So once again, we’re going to lift up the bottom right corner. And once it’s aligned with the top left corner of that seventh square, then again we’re not going to crease all the way. And instead of making a crease within this center triangle, we’re actually going to start on the left side here, And we want to count in 2 triangles from the left side. So 1, 2. And we just want to make a crease within this second triangle here. So we’re just going to push down the paper within that second triangle. Then we’re going to make a small crease. And then we’re going to do the same thing on the right side. So we’re going to count in 2 triangles from the right edge. So 1, 2. And we’re just going to make a small crease within that triangle. So simply flatten out the model within that second triangle. And then make a small crease just like we did on the other side. And once you’ve done that on both sides, then you can unfold. And you’ll see that we’ve made these 2 creases here. Then we’re going to rotate the model 90 degrees, and we’re going to do the same thing. So once again, pull up the bottom right corner, and align it with the top left corner of that seventh square. Then we’re going to count 2 triangles in from the left side, And then we’re going to make a small crease within that triangle. Then we’re going to do the same thing on the right. So count in 2 triangles from the right side. Then make a small crease within that second triangle. And then you can unfold. Then we’re going to rotate 90 degrees once again, and then we’re going to pull up the bottom right corner, up to the top left corner of that seventh square. Then we’re going to make our two small creases within the second triangle on each side. Just like this. And then you can unfold. And again we’re going to rotate 90 degrees. And we’re going to fold up the bottom right corner to the top left corner of that seventh square. Then we’re going to make the two small creases just like we’ve been doing on each side. Then you can unfold. Then we’re going to turn the model over. And now we’re going to make the remaining pre-creases for the tessellation. And we’re going to start by counting two squares up from the bottom right corner, and we’re going to fold the bottom right corner up to the top left corner of that second square. So we’re just going to fold it up, just like we’ve been doing. And once it’s aligned with that corner, then this time we’re going to crease all the way across. Then you can unfold. And now we’re going to count up 6 squares from the bottom right corner. So you should end up in the middle of this square here. And again what we want to do is fold up the bottom right corner, and align it with the top left corner of that sixth square. Just like this. And this time we’re going to make our crease all the way across. Then you can unfold. Then we’re going to rotate the paper 90 degrees, and we’re going to do the same thing. So again we’re going to fold up the bottom right corner to the top left corner of that second square. Just like this. Then you can make your crease all the way across. Once you’ve done that, then you can unfold. And we’re going to fold the same corner up to the top left corner of the sixth square, just like we did before. So again, pull up the bottom right corner. And once it’s aligned with the top left corner of that sixth square, then you can make your crease all the way across. And then you can unfold. Then we’re going to rotate the paper 90 degrees, and we’re going to do the same thing. So again fold up the bottom right corner. Align it with the top left corner of that second square, then make your crease. Then unfold. And we’re going to fold the same corner up to the top left corner of the sixth square, just like we’ve been doing. Then again, make your crease all the way across. And then you can unfold. Then we’re going to rotate the paper 90 degrees one last time. And again we’re going to fold up the bottom right corner, and align it with the top left corner of that second square. Then you can make your crease all the way across. Then you can unfold. Then we’re going to fold the same corner up to the top left corner of the sixth square, just like we did on the other 3 sides. And then you can make your crease all the way across. And then you can unfold. Then we’re going to turn the model over. Again, if you’re using paper with color on one side and white on the other, then the colored side should be up. And once you have this, then we’ve made all of the necessary pre-creases for this tessellation. And at this point, the crease pattern for a single molecule would have looked like this. And this is what the crease pattern looks like for our tessellation with 4 molecules. So again, if you’re expanding this tessellation beyond 4 molecules, then simply repeat this pattern on a larger starting grid. And now we’re going to collapse our first molecule. So as you can see, I’ve marked some new creases here. And what we want to do is lift up the model and pinch these 6 creases from the top. So we’re going to start with these 4 creases down in the bottom left molecule, And we simply want to pinch them from the top to make sure they’re all mountain folds. Just like this. Now if you’ve been following along so far, the creases should already be in the correct orientation. This will just make it easier to collapse the model. Then from here, we want to pinch this mountain fold extending from the right corner of the square. So we’re just going to pinch that from the top as well. And then we’re going to do the same thing with this vertical mountain fold here. So we’re just going to pinch that from the top. And once you’ve reinforced all 6 mountain folds, your model should look like this. And now I want you to notice these 4 small creases that I’ve marked inside this square here. And what we want to do is make sure all of those creases are valley folds. And I find it easiest to do this by bringing both layers on each corner of the square together, just like this. And it helps to do this on all 4 corners at the same time. So you should end up with something like this. And now we’re going to collapse along this square set of valley folds that I’ve marked here. So I find it easiest to do this by putting one finger on each side of this outer square. And then we basically want to push in all of the edges at the same time towards the center of that smaller square there. So we’re just going to push them in like this. And you can lay the model down flat so that it collapses along those creases. And you’ll notice that the model does not lie flat. So what you want to do is pinch this horizontal mountain fold from the top. So we’re just going to pinch it like this. And we’re going to fold it up towards this center horizontal crease. So we’re just going to fold it up like that. Just to flatten out the right side of the model. Then we’re going to do the same thing with that vertical mountain fold here. So we’re basically going to pinch that flap from the top. And then we’re going to fold it over to this left edge here. So we’re just folding it over along an existing crease. And now most of the model should lie flat. So now we’re going to focus on these two flaps down here. And as you can see, we’ve already folded these in the counter-clockwise direction. So we’re going to do the same with these 2 flaps here. So we’re going to fold this left one down and this bottom one over to the right. And once you’ve done that, then you’ve collapsed the bottom left molecule. Then we’re going to rotate the model 90 degrees. And again we’re going to collapse the bottom left molecule. But as you can tell, we can’t see the entire bottom left square. We can only see this rectangle here. So what we want to do is lift up the model. And we’re going to carefully unfold the bottom left portion until we can see that entire square. And as you can see, this partially unfolded our first molecule up here. But it’ll go right back together when we re-collapse the second one. And just like before, our first step is to crease mountain folds along these creases that I’ve marked here. So we’re going to start by pinching this square of mountain folds. So we’re just going to pinch each of those creases from the top, just like this. And you also want to pinch a mountain fold here extending from the right corner of the square. So we’re just going to pinch that crease from the top, just like this. And now you can see that this square is pretty well defined. And now we’re going to create valley folds on these small creases that I’ve marked here. And again, I find it easiest to do this by squeezing together the layers on each corner of the square. Just like this. So we’re just going to work all the way around. It helps to do all 4 corners at the same time, so that your model looks something like this. And now we want to collapse along this square of valley folds in the middle. So again, I find it easiest to do this by putting 1 finger on each edge of the outer square. Then we’re going to push in all 4 edges towards the center of that inner square at the same time, just like this. Then you can put the model down flat just to reinforce those existing valley folds. And your model should look something like this. So in order to flatten it out, what we want to do first is grab this mountain fold from the top. So we’re just going to pinch it like this. And we’re actually going to fold it down to this bottom edge here. So we’re just going to fold it down along an existing horizontal crease. And now we’re going to flatten out the other 3 flaps on this molecule. So this time we’re actually going to fold them in the clockwise direction. So we’re going to fold this bottom flap to the left, just like this. This left flap up, and then this top flap over to the right along existing creases. And if the top molecule is still partially unfolded, then you can grab the flaps from the top, just like this. And then those get folded in the counter-clockwise direction. So just fold them down as they originally were. And once you have this, then you’ve collapsed 2 of the molecules. Then we’re going to rotate the model 90 degrees. And again, we can’t see the entire bottom left square. So what we want to do is lift up the model, and we’re going to partially unfold it until we can see that square. Just like this. Then again we want to make mountain folds on these creases that I’ve marked here. So we’re going to start by pinching the creases on the square from the top. Just like this. And we’re going to work our way around until they’re all mountain folds. Then we also want to make this small mountain fold here extending from the right corner of that square. Just like this. Then we’re going to reinforce the 4 creases that I’ve marked here. So again we’re going to do that by pinching the layers on each corner of the square together, just like this. And it helps to do all 4 at the same time. Then from here, we’re going to put one finger on each edge of this outer square. And then we’re going to push in towards the center along existing valley folds, just like this. Then you can flatten out the model to reinforce those creases. And it should look something like this. Then we’re going to flatten these four flaps by folding them in the counter-clockwise direction. So with this long flap here, we’re just going to fold it up. This bottom flap, we’re going to fold it over to the right. The flap on the left, we’re going to fold it down. And the flap on the top, we’re going to fold to the left. And once you’ve done that, then you’ve collapsed 3 molecules. And now we’re going to rotate the model 90 degrees, and we’re going to do the same thing one last time. Once again, we can’t see the entire bottom left square. So what we’re going to do is lift up the model, and we’re going to have to unfold a few layers just to reveal that entire bottom left square. Just like this. So keep unfolding the bottom left section of the model until you can see this entire bottom left square. And just like we’ve been doing, we want to start by reinforcing these existing mountain folds. So we’re just going to work our way around the square, pinching those creases from the top to make sure they’re all mountain folds. Just like this. Then we’re going to pinch valley folds on these small creases here. And we’re going to do that by squeezing together the layers on all 4 corners of this square. Just like this. So again, it’s easier to do it on all 4 corners at the same time. Until your model looks something like this. Then we’re going to reinforce this square of valley folds. And we’re going to do that by putting 1 finger on each edge of the outer square. And we want to push in on all 4 edges at the same time, just like this. And as you’re doing this, then you can put the model down flat. And it should look something like this. We’re going to fold these 4 flaps down in the clockwise direction, just like this. And then you may have to adjust the other molecules which got partially unfolded. So we’re just going to fold all of the flaps in the correct direction, just like this. And once you’ve done that to all 4 molecules, your model should look like this. If you turn it over, it should look like this on the back side. Then we’re just going to flip it right back over again, and now you’ve done all of the difficult collapsing for this model. So all that’s left is to shape the molecules. So we’re going to start with this bottom right molecule here. And make sure the flaps are turning in the counter-clockwise direction. And we’re going to start by folding this top left flap over to the right. So we’re just going to fold it over to the right along an existing vertical crease. Just like that. And then we’re going to make a crease that extends between this bottom point and this point here where the vertical and horizontal creases intersect. This line should make it a bit easier to visualize. Then what we want to do is lift up on this very top layer of paper. And we’re going to pull it over to the left like this. Then what you want to do is put your finger inside of this pocket as far as it goes. And you want to push down, just to mark the top of that crease. And now you want to extend this edge to this bottom point here. So we’re just going to adjust the edge by pulling it over to the left like this. And once it connects both of those points, then you can make your crease all the way across. Just like this. And then you’ll see that you have these two layers which don’t lie flat. So what you want to do is pinch the layers from each side, and push them in towards one another. You’ll see it will re-collapse along an existing crease from the left side. Then what we want to do is fold this remaining flap over to the left as far as it goes. Just like this. Then you can flatten out the model. And it should look like that. Then we’re going to rotate the paper 90 degrees. And we’re going to do the same thing. So again, we’re going to start by folding the top left flap over to the right. And then we’re going to make a crease that connects both of these points. So we’re going to do that by lifting up on this top layer of paper. And we’re going to pull it over to the left like this. Then you want to put your finger inside of this pocket as far as it goes. And push down to mark the top of that crease. Then from here, you want to adjust that edge until it reaches this bottom point here. And once both of those points are connected, then you can make your crease. Then we’re going to flatten out these two flaps here by bringing them in towards one another, just like this. You’ll see it will re-collapse along an existing crease. Then we’re going to fold this remaining flap over to the left as far as it’ll go. Then you can flatten out the model, and can see that you’ve done that two times. Then we’re going to rotate 90 degrees once again, and we’re going to do the same thing. So again we’re going to fold the top left flap over to the right. Then we’re going to lift up on this top layer of paper, pull it over to the left, and then we’re going to connect both of those points with a crease. Just like this. Once you’ve done that, then you can make your crease all the way across. Then you can pinch these layers together and fold the remaining flap over to the left. Flatten it out. And then you’ve done that 3 times. Then we’re going to rotate one last time and do the same exact thing. So again, we’re carefully going to pull this flap over to the right, without making a crease. And we’re going to lift up this top layer of paper. Again, put your finger inside and connect both of those points with a crease. And once they’re both connected, then you can make your crease all the way across. Then we’re going to flatten out these layers by squeezing from both sides. And then we’re going to fold the remaining flap over to the left. Then you can flatten out the model. And now we’ve completed one of the molecules. So now we’re going to shift down the model, and we’re going to do the same thing on this top left molecule here. Except you’ll notice that the flaps are going in the clockwise direction unlike the first molecule where the flaps were going in the counter-clockwise direction. So for this one, we’re going to start by folding this top flap down. Just like this, along an existing horizontal crease. Then we’re going to make a crease that extends from the top right corner down to where the left edge intersects with the horizontal crease. So we’re going to do that just like we did before by lifting up on this top layer of paper. So we’re going to pull it up like this. And then you carefully want to connect both of those points with a crease. Then you can make your crease all the way across. And then we’re going to flatten out these flaps here by bringing them in from both sides. You’ll see it will re-collapse along an existing crease here. And then we’re going to fold the remaining flap up as far as it goes. Then you can simply flatten out the model, and it should look like this. Then again, we’re going to rotate 90 degrees, and we’re going to do the same thing. So we’re partially going to fold down that top flap because you don’t want to make a crease here. Then we’re going to lift up on this top layer of paper and connect the two points just like we’ve been doing. Just like this. And once both points are connected, then you can make your crease. Then you can push in these layers from each side. And we’re going to fold the remaining flap up as far as it goes. Then you can simply flatten out the model. And we’re going to rotate and do the same exact thing. Again, slightly pull down that top flap, lift up the top layer, and connect both of those points with a crease. Once both points are connected, then you can make your crease. And you can flatten out these layers by squeezing them from each side. Then we’re going to push the remaining flap up as far as it goes. And you can flatten it out. And your model should look like this. Then we’re going to rotate one last time and do the same thing. So slightly pull down this top flap, lift up on the top layer of paper, and connect both of those points with a crease. Then you can make your crease all the way across. Bring these layers together by squeezing them from each side. Then you’re going to fold the remaining flap up as far as it goes. Then flatten out the model, and you should have this. And now you’ve completed 2 molecules. So now we’re going to do the exact same thing on the bottom two molecules here. And once you’ve done that 4 times, then your Origami Double Spearhead Tessellation is complete! You can also try backlighting the tessellation for a really neat effect. And if you’d like, you should feel comfortable enough to expand this design on a larger starting grid. All you have to do is remember that you’re folding multiple versions of the same simple molecule, and you’ll be able to expand this tessellation to just about any size. I hope you’ve enjoyed this video tutorial on how to fold an Origami Double Spearhead Tessellation Designed by Michał Kosmulski. Feel free to upload photos of your completed tessellation to the YouTube Gallery on my website, or simply upload your photos to Instagram with the hashtag #ezorigami to be featured here as well. Also, be sure to check out more of Michał’s work by visiting his website and Flickr photostream. There you will find many of his other impressive tessellation and fractal designs. And if you liked this video, definitely check out some of the other intermediate origami tutorials featured on my YouTube channel as well! Again, I hope you’ve enjoyed this video. Please comment, rate, subscribe, and thank you for watching!

18 thoughts on “Origami Double Spearhead Tessellation (Michał Kosmulski)

  1. Fantastic tutorial Evan, very clearly explained, as always 🙂 I can wait to give it a try.

    With the bit towards the end, after the initial collapse, when you move to the second and forth molecules, you mention to be careful not to add additional creases, would rotating the model clockwise for these molecules mitigate this?

  2. Hey Evan, is there a book, pdf, with all your models in it? With diagrams or cp's? I once made your logarithmic spiral, and I truly fell in love with some of your models/ tessellations! Thanks Evan.

  3. AWESOME! I did this following along and I made my first tessellation!! Very well explained and your voice is relaxing as Bob Ross!!😂

  4. I've never dared starting working no tesselantions before this video I watched last year. I've bought Allessandro Bieber book since. Congrats, you made a great tutorial here.

  5. Thank You Very Much for great tutorial! I make tessellation the first time and I've done it. Thanks a lot once more

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