From the course: Deke's Techniques (2018-2021)

744 Creating a type 15 pentagon in Illustrator

From the course: Deke's Techniques (2018-2021)

744 Creating a type 15 pentagon in Illustrator

- Hey gang, this is Deke McClelland. Welcome to Deke's Techniques. Now, if you've been watching right along, you know that for the last three weeks, we've been discussing some very special, irregular convex pentagons. And they're so very special because they tessellate and they do so monohedrally, meaning that you just repeat the same shape over and over again. But we haven't drawn a darn thing which must be frustrating, which is why today, we are gonna draw one of those pentagons in Illustrator. And it's gonna be the most complex pentagon of them all, which is Type 15, discovered in 2015, a full 30 years after Type 14. And even though it is very complicated, notice that we have to rotate it 12 times to get all the shapes that we need, it's actually pretty easy to draw. Here, let me show you exactly how it works. All right, so let's see how to create that perfectly tessellating Type 15 pentagon entirely from scratch here inside Illustrator. And so I'm going to advance to the last artboard inside this document by pressing Ctrl-Shift-PgDn here on the PC. That would be Command-Shift-PgDn on the Mac. Now, this pentagon was discovered by these guys, Casey Mann, Jennifer McLoud, and David Von Derau in 2015. So 30 years after that Type 14 pentagon from Rolf Stein. And if you thought it had some pretty specific requirements, this one is more specific still. So again, I've formatted the angles in bold and the sides in italic. And notice that each and every angle is spoken for. So this shape has to look exactly like this, which is why it's so easy to draw. So we just need to take into account this data. And you need to bear in mind that where the sides are concerned, a equals c equals e, so those three sides are exactly the same. And b is the same as 2a, or it could be 2c or 2e, since they're identical. D is not spoken for, but it ends up working out automatically. And it tiles like this, which is much different than anything we've seen before. So whereas with Type 14, we repeated the tile a total of six times, with Type 15, we repeat the tile a total of 12 times. And this is the one and only way that this pattern can work out. All right, so I'll go ahead and turn off that patterns layer for the moment. And I'll partially marquee these shapes right here with a Black Arrow tool, so that I select all this stuff. I don't wanna select the letters because I want those to remain on screen. So I'll go ahead and press the Backspace key or the Delete key on the Mac to get rid of that shape and I'll also get rid of this red line right here. And then I'll build this pentagon once again from scratch, not using the Polygon tool because that would give me a regular pentagon, which is not going to work. Instead, I want the Line tool, which is gonna work out beautifully. And I'll start things off by creating the side associated with b because over time, I've gone ahead and oriented all of these pentagons, as you can see, so that the b side is exactly horizontal. And that's just because it makes the tiles easier to construct in the first place. And so armed with the Line tool, notice that I'm seeing a bunch of smart guides because after all, my smart guides are turned on. If yours are not, then go up to the View menu and choose Smart Guides in order to turn that command on. And then I'll just go ahead and click right about there to bring up the Line Segment Tool Options dialog box. Now, I'm gonna start off with a line that is 400 points long. I just happen to know this is gonna work. But you can go with literally any length you like as long as you can easily divide it by two, so you can figure out the lengths of sides a, c, and e. Now, you also wanna set the angle value to zero degrees, which is exactly horizontal. And then click OK in order to create that first line segment like so. I'm gonna nudge it up a little bit, so I get it in a kind of happier place there. And now, I wanna create side a. And I'm gonna do that by clicking at that exact same anchor point again, so that I start the line from the same location. And I'll just go ahead and take that length value and divide it by two, so enter /2 like so. That'll go ahead and take the length, fairly predictably, down to 200 points. I'm gonna leave the angle set to zero degrees and I'll click OK. And just so I can better keep track of what's going on, I'm gonna click on the second color swatch over here on the far left side of the control panel and change the stroke to, let's say, this shade of green. Anything's fine, just as long as you can distinguish it from side b. All right, now, we wanna rotate it into place by switching to the Rotate tool, which you can get by pressing the R key. And then you wanna Alt or Option-click at that same first anchor point right there in order to bring up the Rotate dialog box. And now, notice that we're told that angle A needs to equal 150 degrees, so that's all you do. Just enter that angle value and press the Tab key. And assuming that the Preview checkbox is turned on, you will see that rotation applied on the fly and then just go ahead and click OK. All right, now, looks like our lines aren't in the best locations, so I'll press the V key to switch back to my Black Arrow tool. And I'll Shift-click on the red line in order to add it to the selection. And I'll just go ahead and nudge these guys over by pressing Shift-right arrow here on the keyboard. And now, I'll just go ahead and click off the lines to deselect them and I'll click on that green line to select it. Now, what we wanna do is create side e, which is right here next door. E is gonna be the same length as a, so we just need to duplicate this guy by once again switching to the Rotate tool, which you can get by pressing the R key and then Alt or Option-click on this left hand anchor point in order to once again bring up the Rotate dialog box. Drop down to the instructions and notice that E needs to equal 90 degrees. And so I'll just go ahead and dial in an angle value of 90 like so. And this time, instead of clicking OK, I need to click on the Copy button in order to create a copy of that line at this new location. All right, now, we need to create side c right here. And I'm gonna do that by switching back to my Line tool. And then I'll just go ahead and click on this far right anchor point in order to once again bring up the dialog box. A length value of 200 points is just fine because after all, c is the same a and e. But this time, we want the angle value to go in the opposite direction, so 180 degrees and then click OK. And that'll go ahead and create the line like so. Now, we need to rotate it into position by pressing the R key to switch back to the Rotate tool. And I will Alt or Option-click on that right-hand anchor point to visit the Rotate dialog box. This is gonna be angle B right here and I can see that because I left the bold B behind, it needs to equal 60 degrees. So I'll just go ahead and change that angle value to 60 like so, and press the Tab key in order to update the preview. Apparently, that's not quite right. And that's because this time, we're rotating in the opposite direction. And so I need to change the angle value from positive to negative like so. At which point, everything looks great and so I'll just go ahead and click OK this time around because this is already a copy. So I'll go ahead and click OK like so. And now, we just need to create the last side, which is d. Now, we have some angle information. D right here is supposed to equal 105 degrees and C should be 135 degrees. But that's gonna work out automatically. All I need to do is switch back to the Line tool. And then I'm just gonna drag from this anchor point to this one. And I don't care that the Heads-Up Display is telling me that the distance value is gonna be 386.37 points, which by the way, is the length of the d side. And that's because I don't have any information on that side. It just does not matter, it has to be right. All right, now, I'm gonna press the V key to switch back to my Black Arrow tool. And I'll Shift-click on each one of these sides in order to add it to the selection, so I now have a total of five sides selected. And now, I wanna join them all together by going up to the Object menu, choosing Path, and then choosing Join. Or you can just press Ctrl-J here on the PC or Command-J on the Mac. And that will leave me with one closed path outline. And now, I'll click on that second swatch and change it to black. A line weight of one point is just fine. And then I'll go ahead and click on this first color swatch, which represents the fill, and I'll select that light blue swatch, which I've named Leed Shape. And that's gonna go ahead and fill the shape as we're seeing here. And now, I'll right-click in the document window, choose Arrange, and choose Send to Back. Or you can just press Ctrl-Shift-[. That's Command-Shift-[ on the Mac in order to move the shape behind all of those labels. And that's how you very exactly create a perfectly tessellating Type 15 irregular convex pentagon, as first discovered by this team of folks at the University of Washington back in the year 2015. All right, now, if you're a member of lynda.com/linkedinlearning, I have a follow-up movie in which I show you how to tessellate this pattern. If you're looking forward to next week, I'm gonna show how to take this Type 15 pattern and express it as a proper tile pattern inside Illustrator and then we'll use it to fill this cow. Deke's Techniques, each and every week! Keep watching.

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