On the octagonal faces, the waves shown in blue, red, and purple are sine waves of varying wavelength and amplitude. The other three waves were each formed by combining two of these component waves by simple addition — wave interference, in other words. All three possible combinations of two component waves are included.
I needed three different types of software to create this. First, Geometer’s Sketchpad was used to create the multiple-wave image itself. Next, with MS-Paint, I cropped the image and converted it into a usable format. Finally, Stella 4d was used to place the image on the large faces of this truncated cube, and create this rotating .gif file.
Of these three programs, Stella 4d is easily my favorite, and it also happens to be written by a friend of mine. Trial version / purchase information for this program may be found at http://www.software3d.com/stella.php.