# The Surprising Shape of Success

#### Dave Honda Wins Art Exhibition Honor with Snapology Origami

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At the Joint Mathematics Meetings in January 2018, middle school math teacher and San Diego MTC member David Honda won first prize in the Bridges Art Exhibition category for Best Textile, Sculpture, or Other Medium. Honda sat down with MTCircular to talk about his prize-winning sculpture, “Dodecahedral 11-Hole Torus,” and the challenge of creating origami structures.

#### What inspired you to start making mathematical sculptures, especially with paper and folding?

I’ve always been interested in origami and in creating things in general. I’m a big fan of snapology—a type of origami that requires the folding of strips of paper to produce origami pieces. When I came across the work of Heinz Strobl (the originator of snapology), I was immediately hooked. I started with models that I found online, and then began to create original models.

#### What math goes into creating your pieces?

Snapology naturally lends itself to investigating polyhedra. The various solids (Platonic, Archimedean, Johnson, etc.) are the perfect blueprints for snapology models. The relationship between vertices, faces, and edges allows me to plan out a project. As my models grew larger I realized that I had to take weight, size, and stiffness of paper into account. In fact, my entry into the art exhibit initially started as an attempt to create a model that had an internal support structure. It was later when I talked with Yana Mohanty, one of our MTC coordinators, that she pointed out the piece’s connection to topology and tori. It’s because of these conversations I’m now exploring concepts like topology and dual solids.

#### How do you plan your pieces?

Most of my work starts with asking those “what if…?” questions. “What if I start with creating circles? Could I then join them and make tube-like structures? What if I try to create two intersecting pieces?” After that I usu-ally have a basic idea of what I want to attempt, but then it’s a lot of prototyping. The piece at the art exhibit was the fourth version of that model. Often what I envision in my mind doesn’t work from an engineering stand-point and I have to rethink it. At some point I’d like to investigate the possibility of computer modeling.

#### What have you been working on since the Joint Math Meetings?

I reworked the 11-holed dodecahedral torus so that Yana could take photos from the inside using a 360 camera. (See first photo) I had to rethink the design so the “holes” would be large enough to accommodate her camera. My other project is unfinished: I’m trying to make two interwoven tori based upon dual solids, in this case an octahedron and a cube. I’m also working on creating kits and tutorial videos for others who are interested in learning about snapology.

MTC is a major influence on my work. As a veteran middle school teacher, I get the chance to explore and revisit math that I haven’t seen since my college days. MTC explorations often inspire ideas for my snapology work. Most importantly, if it weren’t for the encouragement of Yana and David Patrick (also a San Diego MTC coordinator), I never would have entered the JMM art exhibit. It’s because of MTC and its people that I’ve had the opportunity to share snapology with others.

-Interview by Sonya Kohli

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