# Debra K. Borkovitz

I seek to share mathematics in ways that are respectful, intellectually challenging, and joyful, and which especially welcome and support those who have previously been excluded. I push students out of their comfort zones and thus think it's only fair that I regularly push myself similarly. Learning crochet, and then temari, were ways to create interesting mathematical models and also to try crafts that initially I wasn't sure I was going to be able to learn. Now I teach a course, "Exploring Math with Yarn and Thread," and one of my favorite aspects of the class is the way the relaxed, collaborative culture of the quilting bee helps transform the culture of the mathematics classroom.

I was surprised and delighted to discover a truncated octahedron when I first drew the graph whose vertices are permutations on four elements and whose edges connect permutations that swap adjacent elements (the Cayley graph of S_4, generated by (12), (23), and (34)). I had it in the back of my mind for years that I'd like to find a visual representation of this graph, and when I started learning temari -- a Chinese/Japanese craft of embroidery on yarn/thread balls -- I realized this medium would work well. This ball is my second effort, and I am currently working on a third -- experimenting with different color combinations.