The fossil order Receptaculitida occurs from the Ordovician to the Carboniferous, possibly to the Permian (Nitecki et al., 2004 - image above comes from Wikimedia). They are quite spectacular fossils, with a striking geometric arrangement of plates on a globose body. Complete fossils are rare, but we have a reasonably good idea of overall structure.
One end of the fossil (shown above in an image from Gould & Katz, 1975) provided the centre that the plates radiated from (the nucleus), and is the most often preserved section. The other end (the lacuna) appears to have been open at the tip (Nitecki et al., 1999). The plates radiated off a central axis to which they were attached by lateral branches known as meroms.
The relationships of receptaculitids have been debated ever since they were discovered. Various authors have regarded them as giant foraminifera, sponges or algae. Part of the problem is that, as with Stylophora, receptaculitids are a group of fossil taxa different enough from anything still living that authors have disagreed on which end was up and which down. Those who would see the receptaculitids as algae have argued for an orientation with the closed nucleus upwards, while an uncalcified stalk would have attached the organism to the substrate through the lacuna. On the contrary, if receptaculitids are to be sponges, the orientation is reversed - the nucleus becomes the lower, while the open lacuna corresponds to the osculum of other sponges, the ejection point of filtered water. Also, like a palaeontological version of the famous two faces vs. vase optical effect, some authors have seen the meroms as solid branches supporting the plates, while others would see them as hollow canals. Authors have also disagreed about whether the nucleus or the lacuna represented the growing end of the receptaculitid, but the existence of specimens with secondarily fused plates at the nucleus, in contrast with the less calcified plates at the lacunar end, strongly implies that the lacuna is the growing end.
A word of caution at this point - the term "alga" is often a difficult one in palaeontology. It is well-known that the various groups of living algae (green, red, brown, etc.) are a polyphyletic group, with multicellularity arising multiple times from unicellular ancestors. Unfortunately, the characters distinguishing the various groups are usually fine scale features, often at the cellular level. At the macroscopic level, the simple organisation of many algae means that members of different groups may be superficially quite similar in appearance, and may be indistinguishable as fossils. As a result, referring to fossils of completely extinct groups as "algae" often implies a certain degree of agnosticism about their actual relationships. At worst, the term "fossil alga" sometimes seems to be a shorthand for "sessile organism that we haven't a clue where else to put it". In the case of receptaculitids, fortunately, an actual modern algal analogue has been suggested in the form of the Dasycladales, an order of calcified green algae that also possess a radial arrangement of side-branches around a central stem (image above of Acetabularia from here). However, there are problems in attributing receptaculitids directly to Dasycladales, as that would effectively require the nucleus to be the growing end.
Nevertheless, an algal interpretation (whatever that might mean) of Receptaculitida does seem more likely than a sponge. The solid outer casing of receptaculitids doesn't compare that well to the more porous structure of sponges. The question of the life-orientation of receptaculitids is even harder to comment on - while an open lacuna-upward position does seem more appealing if the lacuna is the growing tip, an attached lacuna-downwards position is still not impossible, though receptaculitids would then be perhaps the only group other than grasses to have evolved a basal meristem.
In 1972, Zhuravleva and Myagkova assigned receptaculitids to an association with other Palaeozoic sessile problematica such as Archaeocyatha in a new extinct kingdom Archaeata unrelated to both plants and animals (Rowland, 2001). Archaeocyaths were cup-shaped Cambrian organisms that are now almost universally agreed to be sponges of some form. The concept of Archaeata never gained much recognition outside Russia, though it must be admitted that at least part of this may have been due to the inaccessibility of Russian publications in the West.
The Cyclocrinales are another group of Palaeozoic "algae" found from the Middle Cambrian to the Lower Devonian (Nitecki et al., 2004). Cyclocrinales are superficially similar to receptaculitids, with a similar basic body plan (image of Cyclocrinites from Dry Dredgers. They differ in having a less organised nucleus, generally lacking a lacuna, and branching laterals that come off the axis in certain areas rather than over the entire length as in receptaculitids. Cyclocrinales are more easily accepted as related to Dasycladales, and most authors appear to have done just that.
Gould, S. J., & M. Katz. 1975. Disruption of ideal geometry in the growth of receptaculitids: a natural experiment in theoretical morphology. Paleobiology 1: 1-20.
Nitecki, M. H., H. Mutvei & D. V. Nitecki. 1999. Receptaculitids: A phylogenetic debate on a problematic fossil taxon. Springer.
Nitecki, M. H., B. D. Webby, N. Spjeldnaes & Zhen Y.-Y. 2004. Receptaculitids and algae. In The Great Ordovician Biodiversification Event (B. D. Webby, F. Paris, M. L. Droser & I. G. Percival, eds.) Columbia University Press.
Rowland, S. M. 2001. Archaeocyaths - a history of phylogenetic interpretation. Journal of Paleontology 75 (6): 1065-1078.