Asymmetry
The vast majority of sponges are technically asymmetrical. This means the sponge has no apparent bauplan. The cells of most sponges are only loosely interconnected and can be separated by physical disruption. If allowed to resettle, the separated cells will regroup in a form similar to their original structure. This indicates that there is nevertheless some form of genetic or other molecular signal that determines the overall structure of the sponge. Many sponges have amorphous bodies but display some form of symmetry in their individual subunits, such as the spicules seen in some species.
Radial Symmetry
There are no sponges that display "true" radial symmetry as adults, though there is some question as to whether the common ancestor of sponges displayed radial symmetry. Some species of one of the more primitive classes of sponge, Calcarea, display radial symmetry during development. In these species, the developing sponge forms a circular plate shape with a distinct cross-shaped tetraradial (four-way) symmetry.
Partial Radial Symmetry
Several groups of poriferans, particularly sponges in class Hexactinellida, display partial radial symmetry. Hexactinellids are a class of deep-water sponges containing a silica-based skeleton to keep the animal's body rigid. They are generally flower-shaped and have five or six radial spicules in their skeleton.
Partial symmetry means that there are often numerous asymmetrical offshoots from the main spicule (central structure) and this symmetry isn't crucial for everyday function. In addition to the hexactinellids, several other groups of sponges such as Demospongiae and the now-extinct class Archaeocyatha display this type of symmetry on some level.
False Symmetry
Some species of sponge display false symmetry. This is frequently seen in species of class Demospongiae. These animals display outward symmetry and appear to be bell- or flower-shaped. Despite this appearance, careful analysis of the sponge's interior skeleton and aquiferous system (series of internal tubes) shows that there is no internal symmetry. Thus, this is called false symmetry.