For a simple four or six-sided symmetric design, one can get by with less-than-precise rotation and construction methods—not so with complex designs such as the 36-sided kaleidoscope pattern above.  In this exercise, you'll use a small triangular piece of a photograph to construct a design like the one above.  To begin, we need to construct a right triangle to use as a base for a clipping group.  We’ll then save that triangle as a template so we won't have to repeat this step for future designs.

Constructing a right triangle template:

1.  Open a new image: For this exercise, we’ll use 500 x 500 px, RGB color, white background, 72ppi.  If you want a larger template or one at a higher resolution to use for larger printed works, set the initial image up accordingly.  Turn on the rulers (View>Rulers), and be sure the ruler units are set for pixels (Edit>Preferences>Units and Rulers).

2.  Set foreground and background colors to the default black and white by clicking the default colors icon at the bottom of the tool box.  Get the shape tool and choose the line tool on the option bar.  Set the weight at 1.  Click the left-hand edge of the image at the 250 pixel mark on the vertical ruler.  Hold the shift key and drag across the image to the right-hand edge.  Be sure to stop at the edge of the image so the center of the line segment will be at the approximate center of the image—if you drag beyond the edge of the image, the rotation register will be to the right of center, and your triangle will end up being smaller than you want.  You should now have a straight horizontal line across the image. The line will be on a separate layer named Shape 1.

3.  Drag the Shape 1 layer to the new layer icon at the bottom of the Layers Palette to duplicate Shape 1—its name will be Shape 1 copy, by default.  Make Shape 1 copy active.  Go to Image>Transform Shape>Free Transform Shape.  On the option bar, type in 5 for the angle of rotation, and commit the transformation by clicking the check mark on the option bar.   One of the two horizontal lines (on Shape 1 copy) has now rotated and forms a 5 degree angle with the first (Shape 1). 

4.  Choose the line tool again (it should still be the active tool).  Click the create new shape layer on the option bar and click in the image at about the 480 pixel mark on the top ruler and just below the ruler.  Hold the shift key and drag to the bottom of the image.  This will create a new layer called, by default, Shape 2.  Your image should look like the screen shot below:

5.  Choose the magic wand tool.  Set the tolerance to 0, anti-alias checked, Contiguous checked, and Use All Layers checked (see above screen shot).  Click in the triangular area on the right-hand side bordered by the horizontal line on Shape 1 layer, the rotated line on Shape 1 copy layer, and the vertical line on Shape 2.  This will select a right triangle with the 5 degree angle at the center of the image. 

6.  Set the foreground color to something other than black or white.  Click the new layer icon to create a new layer, and make this new layer active (it will be called Layer 1 by default).  Fill the triangular selection with the foreground color.  Deselect.  Save this file as a template for future use.  Then resave the file as Kaleidoscope, and work on the Kaleidoscope file.

Creating the symmetric photo wedge:  Our goal is to have a wedge that we can copy and rotate to build the design.  The wedge needs to have the following properties: 

a)  The shape of the wedge will be an isosceles triangle.  It will be “pointed” at the center of the image ready to rotate. 

b) The measure of this angle at the center of the image depends on the number of sides in the symmetric design.  Since we are working on a design that has 36 sides, the angle has to be 10 degrees (360 divided by 36).  So why did we construct the initial triangle with a 5 degree rotation? Read on.

c)  The wedge will be filled with pieces of a photo, and it needs to by symmetric with respect to the horizontal axis.  We will make the wedge using two copies of the right triangle we just constructed.  Since the triangle we constructed has a 5 degree angle at the center, the wedge we make from it will have a 10 degree angle at the center.  Skip down to the screen shot below step 10 to see what the wedge will look like.

7.   In the Kaleidoscope file, make the filled triangle layer active (Layer 1).  Choose and open the photo you plan to use in the design (it really doesn’t matter what you use as long as the photo has colors and contrast).  You may either drag the photo onto the Kaleidoscope file, or select a portion of the photo to copy and paste into the file.  In either case the photo or portion of the photo will be on a new layer above the filled triangle layer (Named Layer 2 by default).  I copied and pasted mine; see screen shot below:

8.  Make Layer 2, the photo layer, active.  Do Ctrl-G (Layer>Group With Previous) to clip the photo layer to the triangle.  Use the move tool to move or size the photo until you are happy with the design.  Save your work if you haven’t already done so.

9.  At this point, you should clean up the file.  Get rid of the three shape layers by dragging them to the trash can at the bottom of the Layers Palette.  You should now have the white Background layer, the triangle layer (Layer 1) and the photo layer (Layer 2).  Turn off the eye on the Background layer to hide it.  Make the triangle layer active, and go to Layer>Merge Visible.  This will merge the photo layer and the triangle layer—you will be doing this so many times it is worth leaning the quick-key:  Shift+Ctrl+E.  

10.  Drag the merged layer to the new layer icon to duplicate it.  Go to Image>Rotate>Flip Layer Vertical.  This flips one of the copies of the triangle.  Get the move tool.  Hold the shift key (to move in a straight line) and position the flipped triangle so it fits exactly on top of the other triangle to make the wedge.   Turn the white background on and turn off the bounding box so you can be sure of the fit.  When you are satisfied with the fit, turn the background layer off, make one of the triangle layers active, and merge the two halves of the wedge:  Shift+Ctrl+E.

11.  Theoretically, you could copy and rotate this wedge, but it is easier to use a “bowtie” shape to fill the kaleidoscope.  To get this shape, we need another copy of the wedge.  Drag the merged layer (the wedge) to the new layer icon to duplicate it.  Make one of the wedge copies active and go to Image>Rotate>Flip Layer Horizontal.  Hold the shift key and slide the flipped layer to the left until it just touches the original wedge.  When you are satisfied with the fit, be sure the background layer is turned off and merge the two copies of the wedge: Shift+Ctrl+E.  Save your work.