Foto-TriHexaFlexagon (THF)


Preparing the Program
Preparing Your Pictures
Creating Your Flexagon
Printing Your Flexagon
Folding Your Flexagon

Preparing the Program

This simple flexagon program by Fernando G. Sörensen of Argentina will allow you to create a pictorial trihexaflexagon from three images. [A special thank you to Fernando for this upgrade of the program.]

Create a new folder in a convenient (easily accessed) location on your hard drive giving it the name FotoTHF. Download the file, then decompress as usual to the FotoTHF folder. The Foto-THF program does not have to be installed. The FotoTHF folder will contain all five of the decompressed program files.  If space or access is a problem, you can decompress the program file to a diskette or flash drive rather than to your hard drive and run it from there.

Locate the file fthf.exe in the FotoTHF folder on your hard drive (or on the diskette or flash drive containing the decompressed program files). Click on it, then select Opciones, followed by Idioma, and finally English (USA) to replace the Spanish menu bar with an English equivalent. If the FotoTHF folder is located on your hard drive, you can create an icon on the desktop in the usual way.

Preparing Your Pictures

Before you can begin to access and use FOTO-THF to create the strip of triangles for folding, you must assemble three SQUARE pictures (images) with the SAME DIMENSIONS IN PIXELS. [ When generating the strip, FOTO-THF trims each of the images to a square with a side length that is the SMALLER of the two pixel dimensions of the SMALLEST image. Beginning with square images with the same pixel dimensions will produce the best results. ] The images can be accessed by FOTO-THF from any convenient location.

If any image is not square, you can resize it with Windows 7 Paint or Ultimate Paint (see below) or any other quality graphics program. After Foto-THF trims each of the images to a square, it extracts a regular hexagon from each square and subdivides it into six congruent equilateral triangles. In a regular hexagon, the width to height ratio is 200:173.  If the dimensions of a square image are, say, 240 x 240 pixels, the hexagon will have a width of 240 pixels and a height of  (240)(173/200) = (240)(.865) = 208 pixels. The top and bottom of the square image will be cropped slightly. If you would prefer the crop from the other two sides of a square image, rotate it 90 degrees, then save the rotated image.

Windows 7 Paint

Open Paint by clicking the Start button, clicking All Programs, clicking Accessories, and then clicking Paint. Open the selected image file in the usual way. Use Zoom in and Zoom out on the View tab to see a larger or smaller view of the image and to ensure that the desired portion of the image is visable on the screen.

As usual, you can undo any step in what follows by using Ctrl-Z.

Use Cropon the Home tab to crop each image in turn so only the part you wish is visible.

Use Resizeon the Home tab to resize each image. Remember your aim is to prepare three squares with IDENTICAL pixel dimensions. Focus on changing the SMALLER pixel dimension of each rectangular image (where required) so they are common. Adjust each image precisely to a square. Utimate Paint

Select Options, then Tool Bar to reveal the tool bar. If significant cropping is required, select the desired square area as closely as possible with the Cut Rectangle tool. Select Image, then Crop. A new file containing the cropped image will open. Determine the pixel dimensions of the new image by selecting Image, then Resize. Subtract the smaller of SizeX and SizeY (the horizontal and vertical pixel dimensions) from the larger and divide by two. Record this result and which dimension (SizeX or SizeY) was larger. Select Image, then Resize Canvas. If SizeX was the larger pixel dimension, set or scroll both of the Left / Right options to the result as a NEGATIVE number. If SizeY was the larger dimension, set or scroll both of the Top / Bottom options instead. Thus if SizeX = 244 and SizeY = 254, set or scroll both the Top / Bottom options to -5. On the other hand, if SizeX = 230 and SizeY = 221 whereby the difference is 9, an odd number, set or scroll one of the Left / Right options to -5 and the other to -4. Click Apply, then save the resulting square image using a convenient name.

If your square images do not have the same pixel dimensions, you can resize them with the program. Find the pixel dimensions of each image by selecting Image, then Resize. Set or scroll the dimensions of each of the larger square images, in turn, to the dimensions of the smallest square image. The program will scale the dimensions proportionately as long as Keep Aspect Ratio is checked. Click Apply, then save the resized square images in turn.

Creating Your Flexagon

Run Foto-THF by clicking on its desktop icon (or access the file fthf.exe on your hard drive, the diskette or the flash drive containing the decompressed program files). Click on File and then on Select Picture No 1. Locate, select, then Open your first picture. Repeat for Picture No 2 and Picture No 3 in turn.

There are four options available for the equilateral triangle subdivisions. These can be accessed by clicking on Options. The choices toggle on and off with your mouse. Visit Examples for visual details. The default is gray and together.

To create the strip of triangular images, click on File and then on Generate Foto-TriHexaflexagon (or simply click on the hexagon button that will materialize in the lower left hand corner of the program window). When generation is complete, you will be asked to name the resulting flexagon (JPEG) image file. If you do not specify a location in the file name, the flexagon image file will be saved in the same directory as Picture No 3.

Printing Your Flexagon

Windows 7 users should access Paint as before. Select File, and then Open. Locate the flexagon image file just created, then double click on the file name to open it. Select File, and then Print. When the usual options appear, select Print Setup. Change the Page Size to legal. Leave the Orientation as Landscape. The image does not have to be centered to print appropriately (although you may center it vertically if you wish). Scaling should indicate Fit to 1 Page (the default setting). Click OK. Select File, and then Print.

Ultimate Paint users should select File, and then Open. Locate the flexagon image file, then double click on the file name to open it. Select File, and then Print. Change the Page Orientation to Landscape. Click on Properties, then adjust the paper size to legal in the usual way. Click on OK, then change the Width to 13" (the length will change proportionately when the file is printed as long as Keep Aspect Ratio is checked), then click on Print.

Folding Your Flexagon

Cut out the printed shape. Fold it in half lengthwise along the marked central line as shown below.

[At this point, you can glue the two halves of the strip together with a glue stick or a thin layer of rubber cement.  When the hexagonal shape is complete, there will only be one pair of blank triangles to stick together. The flexagon will be more difficult to open "at first" and harder to flatten during the first cycle. However the result will be more durable and presentable.]

You should now have a single-triangle-wide strip printed on both sides. The front face (in yellow in the figure below) will consist of 10 triangles with pictures (indicated by numbers in the figure). The rear face (in white in the figure below) will have 8 triangles with pictures and two blank triangles, one at each end.

Align the strip as shown below. Fold the right end of the strip consisting of 8 triangles forwards along the line a-b.
Fold the right (lower) end of the strip consisting of 5 triangles (one of them blank) forwards along the line c-d.
Finally fold the last two triangles (on the left in the figure below) of the strip forwards along the line e-f.
You should now have a hexagon with the configuration in the figure below.
To complete the flexagon, lift the triangle with the picture that is beneath the blank triangle up and over it. If the hexagonal picture is scrambled, not to worry! There will be an unscrambled picture on the other side. It all depends on how you oriented the strip when you began. Stick the two blank triangles together with a glue stick.  Flip to the other side of the flexagon. Stick the blank side of the loose or free triangle to the blank triangle directly beneath it.
When dry, your model will be ready for flexing. With the unscrambled hexagonal picture facing you, pinch two adjacent triangles together with one hand (usually the left), bending them along the line between them. Push in the opposite corner with your other hand. The flexagon should open to another picture. If it does NOT open, then shift forwards one triangle and try again. Flex through the sequence of three hexagonal pictures moving forward one triangle each time. (Otherwise, the flexagon will refuse to open.) As you proceed through the first cycle, flatten each hexagonal picture along its edges to facilitate smooth subsequent flexing.

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