Although... Let me check, coinmarketcap... No, at least not yet with this name.
"Sand Dollars" are the relatives of the sea urchins and belong to the order Clypeasteroida.
To put the names into the perspective, we belong to the order Primates, your dog and cat are Carnivora

Image is from the paper [1].
Here you can see that the sand dollars still have radial symmetry with 5-axes, but they also tend to show bilateral symmetry but it's a secondary trait. In biology, it's impossible to suddenly lose the heritage and change into something completely different. You will never find a mammal with a radial symmetry.
As you can see on those X-ray images, internal structures are the same as the structures found in sea urchins.

Image from the Reference [1]
Some species, like this bioculata have openings on their shells (between 2 and 5 openings)

Image from the Reference [2]
Or in the form of the cladogram (family tree) it looks like this:

Image from the Reference [3]
Surprisingly or not, due to low attractivity some new species could be still discovered, like this example from 2017!

Image from the Reference [4]
Reference:
- Mihaljević, M. O. R. A. N. A., Iwan Jerjen, and Andrew B. Smith. "The test architecture of Clypeaster (Echinoidea, Clypeasteroida) and its phylogenetic significance." Zootaxa 2983 (2011): 21-38. pdf
- Stara, Paolo, et al. "Distribution of two Amphiope L. Agassiz, 1840 (Echinoidea Clypeasteroida) morphotypes in the Western-Proto-Mediter-ranean Sea." pdf
- Mooi, Rich, Sergio Martínez, and Sara G. Parma. "Phylogenetic systematics of Tertiary monophorasterid sand dollars (Clypeasteroida: Echinoidea) from South America." Journal of Paleontology 74.2 (2000): 263-281. pdf
- Alencar, Carlos Eduardo Rocha Duarte, et al. "New record of the Six-holed Keyhole Urchin, Leodia sexiesperforata (Leske, 1778)(Clypeasteroida, Mellitidae), from the Brazilian coast, with an updated distribution map." Check List 13.5 (2017): 597-603. [pdf](file:///C:/Users/Aleksandar/Downloads/CheckList_article_21381.pdf)
Thank you for your time. I used only the images from the original papers so you can get the insight into this group of animals with the unusual look.
It's really neat watching these guys move around and eat. They "filter" in food, digest it (can take 2 days), and then shoot it right out with the other "useless" nutrients and such to them.
I save a lot of them when I go to the beach since they wash up so much, but I also have a collection of them (the ones I've found that were already dead).
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