octahedron

This year the annual Bridges Math Art conference was held in Stockholm Sweden. Along with a busy program of lectures and workshops, the art exhibit is always a highlight of the event. There was so much interesting work on display that is hard to select just a few to write about in the blog. I encourage everyone to take a look at the on line gallery available on the Bridges website.

Martin Levin’s brass and aluminum sculture “Altogether II” was particularly fascinating to me because it includes all five of the platonic solids. By using thin rods as lines in 3-D space, Levin outlined the figures so you can see the shapes stacked inside each other. Platonic solids are comprised of faces that are regular polygons and at each vertex there are an equal number of faces meeting. The five Platonic are: Tetrahedrons with 3 equilateral triangular faces at each vertex, Cubes with 3 square faces at each vertex, Octahedrons with 4 equilateral triangle faces at each vertex, Dodecahedrons with 3 pentagons at each vertex and, Icosahedrons with 5 equilateral triangles meeting at each vertex. In Levin’s structure the shapes with triangular faces all share a common face plane, and the solids that have three shapes meeting at the vertices share common vertices.

“Triboid” is a resin sculpture by Alfred Peris that is a ruled surface, which means that on any point of the surface there is a straight line that lies on the curved surface. Peris generates these curved surfaces by taking a 2-D curve with no end points and then projects it into paraboloid of revolution to get a 3-D curve. The resulting sculpture has an elegant organic floral presence.

Susan Happersett

The G19 Artisan Gallery is located in Rockport, Massachusetts. Rockport is a picturesque town known for its art community for almost one hundred years. Historically, Rockport artists are known for their seascapes, but the G19 gallery exhibits art in a wide range of materials, styles and themes. I was so happy when I discovered some amazing geometric metal sculptures.

Dodecahedron and Octahedron

I was able to meet with the – somewhat reclusive – artist who would like to be referred to as Dan H. Dan told me that he first became interested in Dodecahedrons when they were referenced in an episode of the TV series “Doctor Who”. He started out making paper models, but after learning how to weld he found metal a better choice of medium. He quickly figured out that the angles for the pentagons need to be fairly accurate or the shape would not fit together. G19 is currently exhibiting Dan’s Dodecahedrons, Octahedrons, and Icosahedrons. These three shapes are all Platonic Solids. The faces of Platonic solids are congruent regular polygons where the same number of faces meet at each vertex. There are only 5 possible Platonic solids and Mathematicians have been studying them for thousands of years. Dan now uses computer software and laser cutting techniques to cut the metal shapes. The finally fabrication, however, is all done by hand. This gives the sculptures a wonderful organic element. The welded edges have a nice texture and the sides retain the flame patterns of the torch. The juxtaposition of using technology for accuracy of the geometry, but then adding the mark of the artists hand makes these sculptures a great example of how artists can use high-tech tools while retaining control of the aesthetics of their work .