Type species: Fenestella (Archimedes) wortheni Hall, 1857
This genus includes the species:
| Archimedes americanus | Condra & Elias, 1944 | L. Carboniferous (Vis.) | USA |
| Archimedes arcticus | Toula, 1875 | L. Permian | Russia |
| Archimedes ardmorensis | Elias, 1957 | L. Carboniferous (Nam.) | USA (Oklahoma) |
| Archimedes bassleri | McFarlan, 1942 | L. Carboniferous (Nam.) | USA |
| Archimedes bolkhovitinovae | Schulga-Nesterenko, 1951 | U. Carboniferous (Mosc.) | Russia |
| Archimedes compactoides | Condra & Elias, 1944 | L. Carboniferous (Vis.) | USA (Arizona) |
| Archimedes compactus | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes confertus | Ulrich, 1905 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes conicus | McFarlan, 1942 | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes curtus | Schulga-Nesterenko, 1941 | L. Permian | Russia |
| Archimedes distans | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes fosteri | Condra & Elias, 1944 | L. Carboniferous (Nam.) | USA (Ark.) |
| Archimedes fragilis | Condra & Elias, 1944 | L. Carboniferous (Nam.) | USA (Ark.) |
| Archimedes gillulyi | Condra & Elias, 1944 | Carboniferous (Mosc.) | USA (Utah) |
| Archimedes girtyi | Condra & Elias, 1944 | Carboniferous (Mosc.) | USA (Utah) |
| Archimedes indigae | Stuckenberg, 1895 | Permian - Carboniferous | Russia |
| Archimedes intermedius | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes invaginatus | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes kentuckiensis | Conkin & Fuson, 1970 | L. Carboniferous (Vis.) | USA (Kentucky) |
| Archimedes keyserlingianus | (Stuckenberg, 1875) | Permian - Carboniferous | Russia |
| Archimedes khvorovae | Schulga-Nesterenko, 1952 | L. Permian (Art.) | Russia |
| Archimedes kovrovensis | Schulga-Nesterenko, 1951 | U. Carboniferous (Ghzel.) | Russia |
| Archimedes lativolvis | Ulrich, 1905 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes laxiformis | McFarlan, 1942 | L. Carboniferous (Vis. - Serp.) | USA (Illinois) |
| Archimedes laxus | (Hall, 1857) | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes lunatus | Condra & Elias, 1944 | L. Carboniferous (Nam.) | USA (Arkansas) |
| Archimedes macfarlani | Condra & Elias, 1944 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes magnus | Condra & Elias, 1944 | L. Carboniferous (Vis. - Nam.) | USA (Arkansas) |
| Archimedes meekanoides | McFarlan, 1942 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes meekanus | Hall, 1857 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes meekanus conicus | McFarlan, 1942 | Carboniferous Mississippian Visean | USA Illinois |
| Archimedes meekanus distans | Ulrich, 1890 | Carboniferous Mississippian Visean-Serpukhovian | USA |
| Archimedes meekanus proutanus | Ulrich, 1890 | Carboniferous Mississippian Visean-Serpukhovian | USA |
| Archimedes meluzovi | Trizna, 1939 | L. Permian (Sak.) | Russia |
| Archimedes missouriensis | Condra & Elias, 1944 | L. Carboniferous (Vis.) | USA |
| Archimedes negligens | Ulrich, 1890 | L. Carboniferous (Vis.) | USA (Iowa, Illinois) |
| Archimedes nikiforovae | Condra & Elias, 1944 | L. Permian (Art.) | Russia |
| Archimedes oquirrhensis | Condra & Elias, 1944 | U. Carboniferous (Mosc.) | USA (Utah) |
| Archimedes orientalis | Schulga-Nesterenko, 1936 | L. Permian (Sak. - Art.) | Russia |
| Archimedes owenanus | (Hall, 1857) | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes parlaxus | McFarlan, 1942 | L. Carboniferous (Vis.) | USA (Kentucky) |
| Archimedes perminimus | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA (Illinois) |
| Archimedes perpetrabilis | Trizna, 1939 | L. Permian (Sak.) | Russia |
| Archimedes? peskensis | Schulga-Nesterenko, 1951 | U. Carboniferous (Mosc.) | Russia |
| Archimedes proutanus | Ulrich, 1890 | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes pseudoswallovanus | Elias, 1957 | L. Carboniferous (Serp.) | USA (Oklahoma) |
| Archimedes regina | Crockford, 1947 | L. Carboniferous (Vis.) | Australia (Qld) |
| Archimedes remotus | McFarlan, 1942 | L. Carboniferous | USA |
| Archimedes rigidus | Elias, 1957 | L. Carboniferous (Serp.) | USA (Oklahoma) |
| Archimedes spiralis | Crockford, 1947 | L. Carboniferous (Vis.) | Australia (Qld) |
| Archimedes stoyanowi | Condra & Elias, 1944 | L. Carboniferous (Vis.) | USA (Arizona) |
| Archimedes stuckenbergi | Holtedahl, 1924 | Permo-Carboniferous | Russia |
| Archimedes sublaxus | Ulrich, 1890 | L. Carboniferous (Vis. - Serp.) | USA (Illinois, Kentucky) |
| Archimedes swallovanus | Hall, 1857 | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes swallovanus communis | Ulrich, 1890 | L. Carboniferous (Vis. - Nam.) | USA |
| Archimedes symmetricus | McFarlan, 1942 | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes tenuatum | Schulga-Nesterenko, 1955 | U. Carboniferous (Mos.) | Russia |
| Archimedes terebriformis | Ulrich, 1890 | L. Carboniferous (Vis. - Serp.) | USA |
| Archimedes timanicus | Condra & Elias, 1944 | Permo-Carboniferous | Russia |
| Archimedes tortuosus | McFarlan, 1942 | L. Carboniferous (Vis.) | USA (Illinois) |
| Archimedes tschernyschewi | Stuckenberg, 1895 | Permo-Carboniferous | Russia |
| Archimedes tsninkensis | Schulga-Nesterenko, 1951 | U. Carboniferous (Kas.) | Russia |
| Archimedes utahensis | Condra & Elias, 1944 | U. Carboniferous (Mosc.) | USA (Utah) |
| Archimedes valmeyeri | Snyder, 1991 | L. Carboniferous (Vis.) | USA (Illinois) |
| Archimedes variifenestratus | Schulga-Nesterenko, 1952 | L. Permian (Sak.) | Russia |
| Archimedes volongensis | Schulga-Nesterenko, 1951 | U. Carboniferous (Kas.) | Russia |
| Archimedes williamsi | Condra & Elias, 1944 | U. Carboniferous (Mosc.) | USA (Utah) |
| Archimedes wortheni | Hall, 1857 | Carboniferous (Miss. -Warsaw) | USA |
This information is based upon various sources, but no personal knowledge. I am indebted to the late Alan Horowitz for his compilation, and to Dr. J. Pachut.
I would be grateful for corrections to, or critical reviews of this information. This is not a 'final' version (an impossible ideal), but a working document.
Archimedes terebreformis at Paleontology and Geology of Missouri.
Archimedes wortheni from the Carboniferous of Illinois, USA - at the Museum of Victoria (Prehistoric Life).
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