Frieze patterns are patterns that repeat along a line. A frieze is a strip or band of decorations, often found along the eaves of a building. Representatives of the seven different symmetry types of frieze pattern are show here.

One can determine the symmetry type of a frieze pattern by asking several yes or no questions, as described below. Find the type of each of the seven patterns shown above. (The notation \infty is intended to represent an infinity symbol.)

If there is a vertical reflection,
    And there is a horizontal reflection,
        Then the pattern has type *22 \infty

If there is a vertical reflection,
    But not a horizontal reflection,
        And there is a half-turn,
            Then the pattern has type 2* \infty

If there is a vertical reflection,
    But neither a horizontal reflection
        Nor a half-turn,
            Then the pattern has type *\infty \infty

If there is no vertical reflection,
    And there is a horizontal reflection,
        Then the pattern has type \infty *

If there is no vertical reflection,
    And there is no horizontal reflection,
        But there is a half-turn,
            Then the pattern has type 22 \infty

If there is no vertical reflection,
    And there is no horizontal reflection,
        And there is no half-turn,
            But there is a glide reflection,
                Then the pattern has type \infty x

If there is no vertical reflection,
    And there is no horizontalreflection,
        And there is no half-turn,
            And there is no glide reflection,
                Then the pattern has type \infty \infty