Difference between revisions of "Instructor:Frieze Exercises Solutions"

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<li>  There's  glide reflections, and if we ignore the wavy lines (water?) it is {{group|p1a1}} </li>
 
<li>  There's  glide reflections, and if we ignore the wavy lines (water?) it is {{group|p1a1}} </li>
  
<li> Several possibilities ... </li>
+
<li> Several possibilities for {{group|pma2}} ... </li>
  
 
<li> The composition of two glide reflections is a translation.  </li>
 
<li> The composition of two glide reflections is a translation.  </li>

Revision as of 09:40, 15 September 2008


Frieze Exercises

    • There are vertical and horizontal mirror lines. Two-fold 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. Two-fold 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)
  1. p1m1, pm11, p1a1, p112
  2. There are many possibilities...
  3. 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
  4. There's glide reflections, and if we ignore the wavy lines (water?) it is p1a1
  5. Several possibilities for pma2 ...
  6. The composition of two glide reflections is a translation.
  7. If you were to rotate the border pattern through any other angle, then the resulting border would be at an angle with the original. The only way it could ever match up with the original is by doing a half-turn (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