Conopeum stamenocelloides was named by Gordon and Taylor (2015) [Colony apparently erect and bilamellar in life (our specimens comprising separated unilamellar fragments), with narrow blade-like stems that are thinnest at the lateral margins and at the rounded growing tip. Zooids regularly quincuncially arranged such that longitudinal zooidal series occur in contiguous rows; subovoid, with a large oval opesia bordered by a granular cryptocyst that is widest proximally and almost shelf-like, narrowing along the lateral margins to the distal end where it comprises just a narrow rim. ZL 505-629 (554) mm, ZW 278-344 (308) mm. No gymnocyst apart from vestigial exposures along some zooidal margins; each proximal corner of an autozooid occupied by a triangular kenozooid with granular cryptocyst and small circular opesia. Ooecia not seen. Apparent vicarious heterozooids present; one such broken structure visible on one margin of holotype specimen, with an extensive area of lateral and distal cryptocystal shelf and very narrow ovate opesia. Zooidal communications are via small mural septula. Colony base and ancestrula not seen.]. Its type specimen is IGNS BZ251 and is a 3D body fossil. Its type locality is Tumaio Limestone, Chatham Island, which is in an Eocene transition zone/lower shoreface tuff in New Zealand.