Wile in 3d there are many different kinds of symmetry in the animal kingdom one pattern that seems to exist is that animals that have a nervous system but no brain tend to have Symmetry around a regular 2d polygon wile organisms that have a centralized brain tend to have bilateral symmetry and two sides of symmetry.
In 4d organisms that would have a nervous system but no centralized brain would probably have symmetry around a regular or semi regular 3d solid. They would probably vary in what number of sides they would have with some having symmetry around a regular 3d solid with others having symmetry around a semi regular solid and a large number of sides.
The 4d animals with a brain would probably have symmetry around a 2d polygon with different ones having different numbers of sides of symmetry. Some would probably have three sides of symmetry, others would have four, some would have five and so on but would all have symmetry around a regular 2d polygon. The most intelligent life forms though would probably have a relatively small number of sides of symmetry though as if it had to many sides of symmetry it would take too much brain power to coordinate all its sides of symmetry meaning that it would have less brain power left over for figuring things out.