Summer of Math Exposition

This interactive “2D Tessellation Explorer” turns tessellations into a hands-on investigation. Load a Shape Workshop with triangles, squares, pentagons, hexagons, octagons, or dodecagons, then drag and arrange pieces to see what locks perfectly with no gaps or overlaps. Hints scattered throughout help explain what to look for. Start with exploring what regular tilings are possible (like 6 triangles, 4 squares, or 3 hexagons) and then experiment with semi-regular mixes - e.g., squares with octagons - to uncover patterns and see what can't work. A Custom Builder lets you pick up to three shapes (20 of each) to search the space of possibilities, including the eight classic semi-regular tessellations. It’s exploratory first, proof-minded second - students feel the constraints before they formalize them. The exploration focuses on visual shapes so that it can be used with young students - older students can use it to try things out before confirming the angles manually, but the angles were mostly left out of this activity to avoid intimidating young pupils.