Concentricycloidea
Found them. In fact, it's more than a new order, it's a new class of echinoderms discovered in 1986 off the coast of New Zealand. Familiarly known as "sea-daisies." In order not to unduly slow the loading of the page, you can find a picture here (look for Xyloplax) and a little bit of information here. The former source states (erroneously, I think) that the Concentricycloidea are now thought to be part of the Asteroidea. (As though anyone here really cares--but it is very cool.)