Ray, there is no symbolism involved at all. The natives had a very good concept of geometry, and used many designs. Some designs came from European sources, particularly floral type work. Remember, beads were foriegn to the natives, and they were shown by the traders what the possibilities of them were.
Many designs later gathered names, such as hourglass for the main design element on this particular case. But they are only descriptive, not symbolic.
The same goes for color representations. If colors were for more than contrast, all the beadwork we see would be solid blocks of red, assuming the particular project was something considered sacred. I've seen many items ochered red for symolism, but always over some other decoration or design element.
They also had a very well developed concept of visual art, and had an inate knowledge of the color wheel of modern artists. If you look at old beadwork, the colors next to each other tend to be across the color wheel for the most contrast, or closely mated to give a smooth blending of colors.
A lot of the symbolism people are looking for, was invented by such people as Ben Hunt in the twentieth century, I believe.
You get into symbolic representation with such things such as the Blue Deer, and Double Woman designs. These are representative of clans, cliques, and factions within the tribe, and are not truly standardized, although almost always design related. All of these are of a pictograph type design, and are easily recognizable as what they are.
Keep in mind, most of the beadwork you will see in museums, was actually made for the tourist trade, and were meant to be appealing to the eye. The same can be said of modern pow wow dress, as form and flash are an important element.
This is just my take on it, from working with this stuff for over thirty years. Keep in mind though, I specialize in Plains and Intermontane Indian Art, and there may be other opinions on this in the East. However, I do not recall ever seeing any primary or empirical sources stating otherwise. If someone does have a source of this type, please post the location or reference. Careless researchers, such as Hunt, Thomas Mails, and a few others have put a lot of questionable publications out over the years, that some take as gospel.
Hopefully, Tipis will drop in and give her two cents, as she is also a professional Indian hobbiest.