{7,3} Surfboard

{7,3} Surfboard

For our tenth anniversary, Sarah Nemec-Nelson planned a perfect gift, a custom surfboard that I could decorate with mathematical art.  We've spent a lot of time in Galveston the last few years, and I've really enjoyed learning to surf.

I've been tuning a number of ideas, finally settling on this.  The surfboard deck will look like the left portion of the image.  The pattern used is on the right.  It is the {7,3} hyperbolic tiling in Vladimir Bulatov's band model, along with a gray outline of its {3,7} dual and a colorful Coxeter complex.  Like the Poincaré disk and upper half plane, the band model is a conformal model of the hyperbolic plane.  The coloring is based on ideas developed with Henry Segerman for our paper Visualizing Hyperbolic Honeycombs.

The surfboard will be shaped by James Fulbright of Strictly Hardcore Surf Specialties, and BoardLams will do the printing (on fiberglass).  I'm stoked!  I'll be sure to post pictures of the end result.

Relevant Links

Vladimir's band model
bulatov.org/math/1001

More on the band model, by Jos Leys (in French, but google translate helps)
images.math.cnrs.fr/Ringworld.html

Visualizing Hyperbolic Honeycombs
arxiv.org/abs/1511.02851

Strictly Hardcore Surf Specialties
www.surfspecialties.com

BoardLams
www.boardlams.com