Day 24

Math 444, Monday, 11/21

Definition of a Symmetry T of F as an Isometry T for which T(F) = F.

Group Property of Symmetries of a Figure - product of two symmetries is a symmetry

Dihedral group as consequence

• Product of two line symmetries is a rotational symmetry (intersecting lines)
• Number of lines = number of rotations if line reflections are symmetries
• Rosette group - rotations possible without line reflections. For a finite set, all the rotations have the same center.

References: There are many, many places on the web that discuss symmetry. The dihedral groups and the rosette groups are often called point symmetry groups. (Though "point symmetry" for a figure usually means that the figure has a point reflection as a symmetry.)

Symmetry Groups of Plane figures (from Scotland)

Wikipedia on dihedral group