Symmetry through the microscope tends to be reduced to two dimensional symmetries. There are basically two classes of symmetries. There are rotational symmetries and organizational symmetries. Crystals and regular geometric forms have symmetries where on one or two axis rotations the positoions are indistiguishable. these include two-fold, three-fold, four-fold, five-fold, six-fold, mirror, and point symmetries. Many life-forms have symmetries where a part is approximately mirrored by other parts of the structure. Leaves are a common example. one side is duplicated on the other side across from it. This is not a rotational symmetry. Rotating the leaf on its symmetry axis would first exchange the top of the leaf with the bottom of the leaf, which is not equivalent. It is a type of approximate mirror symmetry. The symmetries detected may help identify a crystal system or a life form.

A cube has has 4 two-fold axes. A rectangle has 2 two-fold axes. These are rotation symmetries. Many life forms are bisymmetric. They critically have a one fold axis where right and left sides are approximately duplicated. A pinate diatom may have as many as three bifold symmetries.