What are the characteristics. If the fossils of a fern

This is french not science get your categories right.

The rhizome is the stem of the fern plant. It comes in 3 basic forms:

An erect rhizome, which is a solid mass that gives rise to a tuft of fronds. You can see this type of rhizome on a king fern or a crown fern.

A laterally growing rhizome that creeps along or under the ground. It may even climb up a tree. Hound's tongue and thread ferns are examples of a fern with a creeping rhizome.

A vertical rhizome. This can grow into a short or a tall trunk. The trunk of the ponga (silver fern) is a vertical rhizome.