Shannon, there's a name for this style of vintage furniture, and it's called "waterfall." I'm not sure how or where the term originated, but probably it's because the thin sheets of veneered wood have a strongly linear grain pattern, and they are usually glued into cross-hatch or geometric shapes. It's associated with the Depression period in the 1930s, when Modernism first arrived in mass-produced American furniture available to the average person through department stores and furniture stores, but I believe it was also sold throughout the 1950s. Sometimes this kind of chest was part of a bedroom set and would typically sit at the foot of the bed. The part of the bedroom set that people like to buy is the dressing table, which often has a huge circular mirror, or triple mirrors.
Here's an ad selling a bedroom set:
This can be an expensive restoration job because it usually involves replacing veneer.
The words "replacing veneer" make me very, very unhappy. My 1840s sleigh bed, ruined in the flood, had gorgeous book-matched crotch mahogany veneer. The restorer took the bed away to work on in August 2011. It's now almost May 2013 and he's still not done with regluing the veneer. And don't ask me about the cost, as I've discovered that it's going to cost me more than buying a replacement. (The problem is finding a replacement.)