Instructor:Frieze Exercises Solutions
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 There are vertical and horizontal mirror lines. Twofold rotational symmetry: centers at both the center of the rectangle as well as at the midpoint of the vertical side (It's a pmm2)
 Vertical mirror lines. Glide reflections. Twofold rotation at the center of the triangle and at the midpoint of the (diagonal) sides. (It's a pma2)
 Vertical mirror lines. (It's a pm11)
 p1m1, pm11, p1a1, p112
 Supposed to draw patterns using this motif for all seven frieze groups.
 From left to right:
 pm11
 p112 : The under and over crossings prevent it from being pmm2
 p112 : The crossings and some of the small triangles break the symmetry.
 pmm2
 There's glide reflections, and if we ignore the wavy lines (water?) it is p1a1
 Supposed to draw four patterns with group pma2.
 The composition of two glide reflections is a translation.
 If you were to rotate the strip through any other angle, then the resulting strip would be at an angle with the original. The only way it could ever match up with the original is by doing a halfturn (ie 180 degrees).

 A, M, T, U, V, W, Y  pm11
 B, C, D, E  p1m1
 F, G, J, L, P, Q, R  p111
 H, I, O, X  pmm2
 N, S, Z  p112
 p111 = <math>F_1</math>; p1a1 = <math>F_1^3</math>; pm11 = <math>F_1^2</math>; p112 = <math>F_2</math>; pma2 = <math>F_2^2</math>; p1m1 = <math>F^1</math>; pmm2 = <math>F_2^1</math>. The subscript 2 means the group has order 2 rotations.
 It is pma2