Teaching Tessellations?

Questions:[br][br]What ideas do you have to flesh this out into a lesson? [br][br]Would your students enjoy these activities more on paper or on a computer? What are the pros and cons of each?[br][br]It's "elementary to produce a 30/30/120 degree triangle on a given leg, yet the code was intricate. What does this tell us about what's "elementary" and what's not?[br][br]After the math is mastered, there's still the issue of designing with intention. How can we teach students to be intentional with their mathematical practices?[br][br]Bonus Questions:[br][br]Can you devise a square trick?[br][br]Can you devise a [url=https://upload.wikimedia.org/wikipedia/commons/1/1b/Lattice_p5-type1.png]non-regular pentagon[/url] trick (or tricks)?

Information: Teaching Tessellations?