Organisms have a variety of symmetries, and in this page,
you can demonstrate them by applying rotations and reflections to pictures of them.
Strictly speaking, this ought to be done with 3D models,
but many of their symmetries are still apparent in 2D projection.
The symmetry groups applied here are the rosette groups, the 2D point groups.
These are C(n), cyclic, pure rotation, and D(n), dihedral, rotation and reflection,
for cycle numbers n.

WARNING! This demo uses inline SVG, so it may not work in some web browsers.

Overlaid-Image Opacity:

Select an Organism:

The pictures in this demo have been edited to give them appropriate orientations and sizes.
They are subject to licenses appropriate for derivative works of the original pictures.

It has been difficult for me to find good pictures for making demos
of the symmetries of these organisms:

Squid: overall D1 bilateral, short tentacles: D8, long tentacles: D2

Octopus: overall D1 bilateral, tentacles: D8

Comb jelly / ctenophore: D2 / D8

Complete sets of this demo's rotations and reflections
are the two-dimensional point groups,
named from how they keep a point fixed.
This demo focuses on these groups because many organism symmetries can take these forms
when projected onto two dimensions, and because they are the easiest to implement.

The two-dimensional point groups can be subdivided in two ways:

Continuous vs. discrete

Pure rotation (cyclic) vs. rotation and reflection (dihedral)

which combine into these possibilities:

Pure Rotation

With Reflection

Continuous

SO(2)

O(2)

Discrete

C(n)

D(n)

Order (# Members)

n

2n

There are n rotations and n reflections.
SO is "special orthogonal", O is "orthogonal".

There are several other symmetries that organisms and their parts may have,
which I illustrate in my Organism-Symmetry Gallery.
It contains many more pictures than I have been able to use here.

Author: Loren Petrich, online as lpetrich, e-mail petrich (at) panix (dot) com