Exercises through illustrate the seven different types of friezes when they are classified according to their symmetries. Imagine the figure shown to be continued infinitely to the right and left. The symmetry group of a frieze always contains translations. For each of these exercises answer these questions about the symmetry group of the frieze. E E E E E E E E E E E E
a. Does the group contain a rotation?
b. Does the group contain a reflection across a horizontal line?
c. Does the group contain a reflection across a vertical line?
d. Does the group contain a nontrivial glide reflection?
e. To which of the possible groups ℤ, D∞, ℤ × ℤ2, or D∞ × ℤ2 do you think the symmetry group of the frieze is isomorphic?
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