Teaching Tessellations?

Questions: What ideas do you have to flesh this out into a lesson? Would your students enjoy these activities more on paper or on a computer? What are the pros and cons of each? 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? 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? Bonus Questions: Can you devise a square trick? Can you devise a non-regular pentagon trick (or tricks)?