 I recently came across this New York Times article on the Einstein tile that I found quite interesting. The article left me hungry for a little more so I followed it up with a YouTube search that brought me to the up and Adam channel where Jade has a great video on the subject and before I knew it I was in the rabbit hole. I won't go deep into the geometry and how it works because Jade does an excellent job explaining it in her video and I'll link her video below but from what I understand there was a 50 year search for a single tile that can tile a plane in a non-periodic fashion meaning the patterns created by the tiling don't repeat. In this video I want to look at how we can design this tile in Fusion 360 and I'll show you some useful techniques with the move tool. The version we're going to look at has been named the hat tile because well it looks like a hat. I actually covered this lesson last week in my weekly Fusion 360 live class. This is an online class where we meet weekly over Zoom and I help you with your Fusion 360 questions and designs. I'm currently running a promotion so if this is something you'd be interested in joining check out the link below. All right let's jump right in. Okay here's our hat tile that we're going to create and if you look closely you can see that this hat tile is made up of these smaller kite tiles and these smaller kite tiles are made up of these triangles. And if we take an even closer look we can see that these four tiles here if we were to continue that pattern we would see that we've got a hexagon here. So that's six kites that make up this hexagon. And if we just take this tile kind of move that here move one over here and then create two additional ones here we'll have our hat shape. So that's kind of the approach I'm going to take here. So let's jump into Fusion and see how to approach that. I'm going to begin by creating a sketch on the XY plane and we're going to come in with a polygon. So here we're going to go to create polygon, circumscribe polygon, start right at our origin. This is going to be six kites we're going to make a hexagon and let me just give it a radius of 25 millimeters here and then I'll take that top edge and constrain it with a horizontal constraint. I'm going to move the dimension off to the side here so we can come in with a line tool. I'm going to grab a line from the center here straight up to the midpoint there. You see that triangle constraint there. I'm going to do the same thing from the origin to the middle of this line here again finding that midpoint constraint and I've got one kite there that I can now begin to build this. Now here I've got some options. I can take this one kite shape here and create a circular pattern to create six of these profiles within the sketch environment. However instead of doing that I'm going to finish this sketch. I'm going to select that profile and extrude it five millimeters to give me one body. It's going to be better here to take that one body and create a circular pattern from that rather than doing it at the sketch level. So we'll go to create down to pattern, circular pattern. I'm going to select my body make sure object type is set to bodies. My axis of rotation is going to be my z axis there. I'm going to select it and then I'm going to go ahead and increase the quantity here to six. Okay and the nice thing about that is it gives me six individual bodies instead of you know one body there. So now I've got these six bodies that I can just simply move around to create my hat. So let me bring that image here again and we can see as I was pointing out before this section here you know is what I have right here and so the first thing I want to do is create this tile here and so what I can do is I can see that this tile here it's actually in the same orientation that I want it to be over here. Let me move this out the way here. So if I take that and I keep that same orientation and I bring it here that'll begin to build this out. So let's go ahead and do that and before I proceed I should actually mention that this lesson is really going to be a lesson on moving bodies versus moving components and I'm going to show both ways. We'll use bodies to create our overall hat tile and then once we have our hat tile I'm going to show you how we're going to convert it into components and use our joint tool to pattern our tiles. Okay so we'll stick with bodies for now. I'm going to right click and go to move copy. I'm going to click to select my body here move object to set to bodies. I'm going to go to free move. I'm going to grab this little widget here the little the square icon there and just move it over here. Now again it is in the same orientation that I need it to be so I don't have to rotate it. I just need it to move to align this edge and to line up with this edge here. So I'm going to select my point to point and here I can either choose you know this corner or this corner here. Let me orbit and just grab that point and say I want that point to move over here and click okay and there we have it. That takes care of that first tile there moved right into place. Okay next let's go ahead and take this tile here and I want this tile to move over here but I do want it to rotate so that this edge here is lined up with this edge here. So let's go ahead and do that. Again I'll approach it the same way right click move copy select my tile and go to free move. I'm going to grab it by the little square here drag it and now I'm going to take my rotation widget here and rotate it but you'll see the center here of my widget that would be the center of rotation so if I start to move that it'll move around that center. I want to move it so that it'll pivot in the middle of the body here so to do that I'm going to go to set pivot and then click anywhere here in the middle I'm just going to roughly estimate the center go back and click that green check mark and now when I begin to rotate it you can see it rotates about where I put that point and here the important thing to remember is this is going to want to rotate in angles of 60 degrees so multiples of 60 so here I know if I get it close to where kind of I want it to be and I'll look at the number and I'll say okay well that's going to end up be you know either being 60 or 120 so and it'll snap to 120 so I'll make sure to stop it right at 120. All right now that I have the angle correct I'll go to point to point and I'm going to say move this point here the top point to this top point here and that brings it right into place. Okay perfect we have these two sections in place and the next one we need to create is this one and then this one here so let's look at how we're going to do that. Okay so I need a tile to come in like this and here instead of moving another tile into place if I take a close look here I can see that if I take this tile and just rotate a copy I can get it to come in pivot around this point right here and I should be able to create a copy and have it land exactly where I want so let's try that. I'm going to right click go to move copy select my tile and here instead of the free move I'm going to go to rotate and it's going to ask me for my axis of rotation for that I'm going to choose this as the hinge. All right now watch this if I just take this little widget and start rotating it I'm going to want to go here let's keep going all right so here I can see 120 looks like it's going to match up right again to 120 so we'll do that and you want to make sure to click create copy here so it brings in a copy of that there we go and we've got one more tile to make and that's this tile here and that tile is going to go right here and if we take a look at that we can see that that would simply be a mirror of this tile here so if I take this tile and just kind of flip it over that would give me exactly what I need so to do that we'll go to create down to mirror I'm going to select my tile come in with a mirror plane as this face right here and I'm going to go with a new body here click okay and there we have it so perfect I was able to create my hat tile here simply by creating a hexagon splitting it into one tile and just moved my tiles around to give me this shape and you can see here I still have all my individual tiles here separated into bodies I'm going to end it here for now but in the next video I'm going to show how we're going to take these separate bodies combine them into one body and then convert that one body to a component and then create multiple components here where we've got our separate tiles here and then I can simply kind of drag them into place and use our joints command to be able to create our tiling here so stay tuned for that that's going to be in the next video if you have any questions on the approach I took today leave it in the comments below I will be uploading the fusion 360 files to my patreon page so if you want access to those files or and if you want to just support my channel consider becoming a patreon all right check out the links I have below to some of my online courses and other resources if you'd like to learn more about fusion 360 I will see you soon