Infinite shapes are fun to design. In this Illustrator tutorial, learn how to create a specific impossible shape: an ‘Infinite Triangle.’ This vector drawing of an impossible object couldn’t be physically constructed, but we can design it in Illustrator in around an hour. You will be using Guides, Gradients, the Rotate Tool, and a simple Transparency Blend for the final touches.
Step 1
Start by creating a new document with the dimensions of 1400 x 1400 pixels and use RGB color space.
Before you go any further, go to the View menu and make sure Show Rulers is selected (Command + R), Lock Guides is unchecked (Option + Commend + 
and that Smart Guides (Command + U) and Snap to Point (Option + Command + “) are both checked. You’ll see why using these settings are useful shortly.
Step 2
Drag out a guide from the left ruler and set its X-Value to 300 pixels in the top contextual menu. As you’ve set guides to unlocked, you can select and move them once created if you need to adjust their location.
Step 3
Now you need to duplicate the first guide. With the guide selected, open up the Move Panel (Shift + Command + M), set the Horizontal Position to 400 pixels and click Copy.
You need to duplicate the new guide using the same settings as before. The quickest way to do this is with the keyboard shortcut Command + D.
Step 4
Create a horizontal guide by dragging from the top ruler and set its Y-Value to 1100 pixels.
Step 5
Duplicate the horizontal guide using the same technique in Step 3, only this time you need to set the Horizontal Position to 0 pixels and the Vertical to -120 pixels. Repeat once more with Command + D.
Step 6
With the three horizontal guides selected, choose the Rotate Tool (R), and Option-click the intersect between the middle horizontal and the right hand vertical guides (as indicated). In the Rotate Dialogue Box set the angle to 120 degrees and click Copy.
Step 7
Repeat the process in Step 6, this time selecting the intersect between the new middle angled guide and the middle vertical guide. Use the same 120 degree angle and click Copy.
If you want to keep things organized, Double-click the default layer and rename it “Guides,” lock it and create a New Layer (Command + L) named “Artwork.”
Step 8
Choose the Path Tool (P) and create the shape shown in the screenshot below. It’s important that you follow the highlighted points exactly – the accuracy is made easier as the active Snap to Point displays an ‘Intersect’ when the cursor rolls over each point.
Step 9
With the shape selected use the Gradient Tool (G) to drag from left to right and fill the shape with a gradient.
Double-click the sliders in the gradient panel and set them to the values 10% black and 70% black (see below).
Step 10
Choose the Rotate Tool (R) and Option-click the intersect highlighted below. Set the angle in the Rotate Dialogue Box to 120 degrees and click Copy.
Step 11
Click and Drag the new shape and ‘snap’ the inner corner over the bottom right intersect as shown.
It’s important to get this ‘spot-on’ so zoom in to make sure.
Step 12
Repeat Step 10 only this time Option-click the new intersect point, as shown below.
Step 13
Click and Drag the third shape and snap the inner corner over the top intersect as shown.
Step 14
Select all (Command + A) and add a white stroke of 3 points. Group the objects (Command + G). You can now hide the ‘Guides’ layer.
Step 15
With the grouped shape still selected, Double-click on the Rotate Tool in the Tools Palette. Set the angle in the Rotate Dialogue Box to 45 degrees and click OK. Center the triangle on the artboard if necessary.
Step 16
Still with the triangle selected activate the Reflect Tool (O). Option-click on the very bottom point, and when the Reflect Dialogue Box appears, select the Horizontal Axis and click Copy.
Step 17
With the Rectangle Tool (M) selected draw out a rectangle from the point where the two triangles touch to the bottom of the artboard. The exact dimensions are not crucial, but make sure it covers the bottom triangle as shown.
Fill the rectangle with a gradient using a -90 degree angle and set the slider color values as shown below (60% black and red 0, green 0, blue 0). It’s important that the right hand slider is set to an RGB black and not a Grayscale black, otherwise the next step will not be as effective.
Step 18
Select both the rectangle and the bottom triangle, then create an Opacity Mask by selecting it from the Transparency Panel sub-menu.
Step 19
With the Rectangle Tool (M) draw out a square of 1400 x 1400 pixels that covers the entire artboard, then send the object to the back (Shift + Command + Left Bracket key).
Fill the square with a 90 degree gradient and set the slider values to 30% black, 5% black and 20% black (see below). Set the Location of the middle slider to 40%.
Finished!
Your completed impossible triangle shape should resemble the following infinite vector drawing. For simplicity I’ve used black gradients in the example, but obviously you could add a bit of color if you have the urge.
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