# Scott Vorthmann

I am fascinated by Algebra, and how it manifests as symmetry and form. All of my work derives from my experience building vZome, a program for geometric modelling based originally on Zometool. vZome has led me to explore more generalized algebraic fields, each extending the field of rational numbers with one or more irrationals, to achieve particular symmetries in 2-D, 3-D, and higher dimension vector spaces over the fields. The art that I create all derives from this aesthetic of computing exactly with integers, yet achieving surprising structures and symmetries. In my work I also try to highlight the beautiful serendipity that often arises in working with algebraic structures -- things seem to just "line up nicely".

This piece was inspired by my work with David Hall and David Richter, exploring the Chord Ratio Construction for generating points on quadric surfaces. The two paraboloids are identical, though one has been colored to illustrate the "zones" (families of parallel lines). The paraboloids are polyhedral: each face is an affine-regular hexagon, strictly following the rule of a diameter twice the length of the parallel edges. Starting from three initial edges, following the rule defines an infinite polyhedron, with all vertices lying on a paraboloid, while all faces are truly planar. Using a very specific kind of reflection, the figure contains all the symmetries normally associated with the reflection group of a hexagon tiling.