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Drawing nine base hexagons

From: Designs dekeConstructed: Animating a Mind-Bending Illusion

Video: Drawing nine base hexagons

In this chapter we'll create this impossible so-called Penrose triangle,

Drawing nine base hexagons

In this chapter we'll create this impossible so-called Penrose triangle, in which each edge tucks behind another. So that no side is entirely in front or in back of the shape. In this movie we'll start things off by creating this collection of nine hexagons, which will inform the alignment of the edges. Now, if you're working along with me, which I hope you are, then you want to go ahead and launch Adobe Illustrator, and then confirm a couple of settings by going up to the View menu.

For starters, make sure your smart guides are turned on. If they're not, go ahead and choose the smart guides command. And then notice here, below the Rulers command. We have a bounding box item. It should read Show Bounding Box, which tells you that the bounding box is turned off. If it reads Hide Bounding Box instead, then go ahead and choose the command to get rid of the bounding box because otherwise it will get in our way. Now we'll be creating this file from scratch, so go up to the File menu and choose the New command, or press Ctrl + n or Cmd + n on the Mac.

Then inside the new dialogue box, go ahead and change this very first profile option to Web. So that we're working in the rgb color space. And our units are set to pixels. Then change the width value to 700 pixels. And take the height value up to 600 pixels. Now we need to make one more modification. By clicking on the triangle in front of the word Advance. In order to expand this region. And then, turn off Align New Objects to Pixel Grid, because if you leave that checkbox turned on, you're going to have some severe alignment problems.

And then click OK. Now, I'll go ahead and zoom in by pressing Ctrl + plus or Cmd + plus on the Mac, and I'll go over here to my shape tool flyout menu. And I'll choose the Polygon Tool. Next you want to click somewhere in the lower left region of your document in order to bring up the polygon dialog box. By default the number of sides is set to six which is exactly what we want. But I need a higher radius value. In fact, when everything is said and done I need it to be 70 pixels like so.

And then, click OK to create that hexagon from the center outward. And now, what you want to do is go up to the horizontal control panel, all the way over here on the left hand side, click on this Fill icon, and go ahead and switch it to None. Now, go ahead and select the black arrow tool which Illustrator calls the Selection tool. And you can get to it by pressing the v key. And now, you can either double click on that tool icon or, just press the Enter key, or the Return key on the Mac, to bring up the Move dialog box.

Then change the Horizontal value to 300 pixels, leave the Vertical value set to 0 pixels, and turn on the Preview checkbox. And you'll see that the hexagon goes ahead and shuffles over to the right-hand side of the screen, at which point click on the Copy button in order to create a copy of that shape. Now press Enter or Return to once again bring up the Move dialogue box and drop down to the angle value right there and change it to 120 degrees. And assuming that the preview check box is still on you should see the shape jump to the top of the document.

And assuming that the preview check box is still turned on and the distance value still reads 300 pixels, you should see the shape jump to the top of the document, in which case go ahead and click copy once again. Now press the Enter or the Return key a third time to once again bring up the move dialogue box. And after confirming that the distance is set to 300 pixels, change the angle value to negative 120 degrees, and that will create yet another polygon down here in the lower left corner. At which point click on the copy button in order to create a copy of the shape.

So in other words, we have a total of four hexagons. With one sitting on top of the other down here in the lower left corner. Now, you'll want to press Ctrl + a or Cmd + a on the Mac in order to select all of the shapes. And then, go up to the Object menu, choose Blend, and choose Make. Or you can press Ctrl + Alt + B or Cmd + Option + B on the Mac. At which point, you'll most likely see one intermediate hexagon between each selective pair.

I actually want two, so go ahead and return to the Object menu choose Blend, and then choose Blend Options to bring up the Blend Options dialog box. Then turn on the preview checkbox, change spacing to Specified Steps and increase that value right there from 1 to 2 in order to produce this effect here. And then go ahead and click OK. Now, when we want to center these shapes inside of the art board. And before you can pull that off, you need to go up to the object menu and choose the Group command.

Or press Ctrl + G, or Cmd + G on the Mac. Then, go up here to this align to selection icon, and click on it. And change it to Align to Artboard. And now, click on the second icon in, Horizontal Align Center. And then click on the fifth icon, Vertical Align Center, in order to exactly center those shapes inside the art board. So that is how you create the nine hexagons that we'll need to serve as guidelines for our initial impossible, Penrose triangle.

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