# Polyhedra, fractals, and tessellations are all a part of Maker Studio.

The focus of this block in Maker Studio is mathematical making: polyhedra, fractals, tessellations, geometric designs, and more. Not surprisingly, such activities are particularly exciting with Proof School students. When I ask what it means for an octahedron to be stellated, multiple hands shoot up. When we work with compasses and straight edges, impromptu math investigations happen.

We spent our first two weeks building the platonic solids in three ways. Physically manipulating and constructing these fundamental polyhedra helps us build intuition about their form, their patterns, and the remarkably simple constraints that define them.

We started with balloons. How many continuous balloons does it take to build a tetrahedron? A dodecahedron? Can you prove it? The solution is a cute application of graph theory.

Next, we built platonic solids out of file folders, drafting their nets ourselves. Imagine a cube, slit at some edges so that it unfolds into a continuous two-dimensional shape. How would we draw a shape that folds into an octahedron? An icosahedron? One ambitious sixth grader even managed to construct a cuboctahedron.

Finally, we spent two classes working on modular origami: folding many identical pieces that come together to form an ornate polyhedron. On our second day of folding, we folded while watching Between the Folds--a fascinating documentary about the art and science of origami. As we dabble in a range of activities, it’s inspiring to be reminded of how deeply one can dive into a single art form.

This block’s activities mark a departure from past blocks. For the first time, precision really matters. Some projects require far more diligence and patience than we’ve needed before. We need to think carefully as we work, as we have a specific end goal in mind. Our middle schoolers have risen to the challenge beautifully.

--Kathy Lin