View source

{{Exercises}}
<ol>
<li>Copy (or print out) these simple frieze patterns, and mark all symmetries for each pattern. That is, identify and mark all translations, rotations, reflections and glide-reflections if present.
  <ol style="list-style-type:lower-alpha">
    <li style="padding:12pt">[[Image:ladder.svg]]</li>
    <li style="padding:12pt">[[Image:zigzag.svg]]<p></p></li>
    <li style="padding:12pt">[[Image:moons.svg]]<p></p></li>
</ol>
</li>

<li>
Identify the symmetry group for each of these frieze patterns:
  <ol style="list-style-type:lower-alpha">
    <li>[[Image:ngaru.svg|500px]]</li>
    <li>[[Image:stlcb-pm11-4.jpg|500px]]</li>
    <li>[[Image:bear-tracks.svg|500px]]</li>
    <li>[[Image:dna.jpg|500px]]</li>
</ol>
</li>

<li>Use this motif to draw seven frieze patterns, one with each symmetry group:
[[Image:simple-motif.svg]]
</li>
<li>
Consider the four colorful strip patterns that Escher found in Ravello, Italy ([[Designs from Ravello]]).<br>
For each pattern, identify which symmetries are present (all have translational symmetry, but state if the border has rotational, refelctional and/or glide reflectional symmetry). Use this information to decide which frieze symmetry group it has.  You can ignore colors.
</li>
<li>What is the symmetry group of the frieze pattern on {{VOS}} Page 42?</li>

<li>Draw four patterns with the symmetry group pma2.  Make them look as different as possible.  Be creative.</li>

<li>In a frieze pattern with a glide reflection, explain why the glide reflection is always half the length of the shortest translation.</li>

<li>Explain why a frieze pattern can have only 180° rotations.</li>

<li>
  <ol style="list-style-type:lower-alpha">
   <li>What frieze symmetry group do you get if you write a row of A’s?  B’s?
          Answer this for all 26 capital letters by listing the letters that correspond to each symmetry group.  Use the alphabet below:
          [[Image:alphabet.svg]]
    </li>
     <li>Compare with your answer to [[Rosette Exercises#alphabet]].  Do letters which had the same rosette symmetry group make
            frieze patterns with the same symmetry group?
</li>
</ol>




[[Instructor:Frieze Exercises Solutions]] (restricted access)