Use this activity to recognize dihedral symmetry and reflections in figures and examining various symmetries.
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All shapes in a figure are identical. The black shape is the seed shape. If you click and drag any of the red vertices of a black shape, it will alter both the black shape and all the identical blue shapes. For the best figures, try to keep the shapes from overlapping.
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A dihedral figure is one with rotational and reflectional symmetries. If you look at the top left image in the activity, you'll see it's labeled "Dihedral 2." This is because it has two symmetries, horizontal and vertical. The Dihedral 3 figure can be turned in 3 ways and reflected in 3 ways, and so forth.
Each figure in the activity has a different type of dihedral symmetry. Use the red vertices to change their shapes. As you alter the figures, try to answer these questions:
- Are the figures always symmetrical?
- Do the kinds of shapes used to make the figure determine the kind of symmetry?
- Can you find all the rotational and reflectional symmetries?
- Some figures have an odd dihedral symmetry, such as the one in the top right, while others have even dihedral symmetry. What do all odd dihedral figures have in common that's different from the even dihedral figures?
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