While it sounds like a single celled organism, a glamelia is in fact a large man-made flower. Often called composite flowers or duchess roses, they are hand-wired or glued into a single bloom from the individual petals of many flowers. In the 40’s and 50’s the popular camellia bloom was expensive and hard to come by. So the crafty folks of the time glued gladiolas petals to a cardboard circle to create a camellia like bloom. Thus gla-melia. Nowadays glamelia are typically wired petal by petal into the finished shape and are not as flat. They are also comprised of many different varieties of flowers.
While incredibly beautiful, they are complicated and therefore expensive. I’m guessing that’s why they never get super popular despite being gorgeous and carried by celebrities like Katherine Heigl at her wedding. In addition to being very time consuming to make, large glamelia typically take 30-50 flowers to create. If you chose a flower with a lot of petals (like a rose), the price is a lot more agreeable than one made of orchids (which are independently expensive and have very few petals). Also make sure that your chosen petals do well outside of water and are not easily bruised. Lastly, these bouquets are fragile so it’s not a toss bouquet!