Interesting, the name Archimedes for this fossil came from the writings of David Dale Owen who credited the name's origin to Charles-Alexandre Lesueur (French naturalist-artist) who was at New Harmony with Robert Owen, William Maclure, Thomas Say and Gerard Troost.
If you visit New Harmony, look at the weather vane on top of one of the original laboratory buildings. It has a blastoid and Archimedes bryozoan on it.
I read something in a scientific journal where two researchers were speculating that the Archimedes and Fenestella bryozoans might be two separate entities instead of one as shown on these next two images. It looks to me that the bryozoan netting had attachment places on the threads of the screw shape. So it would look like it was all part of one creature. It is possible I read something wrong as well.