# dodecahedron

# Platonic Solids in Rockport, Massachusetts

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.

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 .

— Susan Happersett

# Bridges Math Art Conference Seoul – Part 2

I have just returned from an amazing visit to Seoul to participate in the Bridges Conference. Bridges is an international organization that promotes the connections between Mathematics and Art, Music, Architecture, and Culture. This year the conference was a satellite conference for the huge International Congress of Mathematicians that took place in Seoul during the same week. This proximity enhanced our events by bringing numerous renowned Mathematicians (including Fields Medal winner Cedric Villani) to speak at the Bridges conference. One of the highlights of this conference is always the Art Exhibition. There was so much exciting work on display but I will only be able to discuss a small percentage in my blog.

#### Gary Greenfield

There is a type of computer assisted painting referred to as Ant Paintings in which points of pigment are deposited on a surface using an algorithm that determines when the pigment is picked up, where it is carried and where it is dropped. This process of “mobile automata” mimics the natural behavior of ants moving grains of sand. The completed paintings have an organic quality. Gary Greenfield has created a new series of work using this technique. He is the first artist to explore the incorporation of formulae into the algorithms in such a way that geometric shapes are formed in the painting.

In the digital print “PCD #11863”, Greenfield starts the process with uniformly distributed grains of pigment. Then the virtual ants are instructed to carry and deposit the color on to twelve polar curves. Polar curves are curves drawn using the polar coordinate system. This is a 2-D coordinate system like the Cartesian coordinate system, but instead of having two axis to define the placement of a point on the plane, the Polar Coordinate system uses a single fixed point, an angle from a fixed direction, and the distance from the initial point, to determine the placement of the point. For this particular painting Greenfield used the formula

to determine where the pigment would be distributed The resulting image has order four rotational symmetry and a graceful use of concentric shapes, but what makes this work unique to me is its organic quality.

#### David Reimann

There was one sculpture in the exhibition that I felt was a great visual representation of the whole conference. “Mathematics is Universal” is a wooden dodecahedral form by David Reimann.

A regular dodecahedron is comprised of 12 regular pentagons (regular means all sides have the same measure), and 30 edges. The sculpture “Mathematics features the 30 edges of the dodecahedral form made out of wood strips. Each of the 30 strips has the word mathematics hand-painted in a different language. I feel this sculpture is a perfect metaphor for our conference. People from many cultures gathering to discuss the beauty and form of Mathematics.

#### Suman Vaze

Some of the most abstract and gestural art on view was by the painter Suman Vaze. Her canvas “Ryoanji III” is an expression of the balance found in a 4 by 4 magic square. It is divided into a 4 by 4 invisible grid, and the number of horizontal and vertical lines going through a section of the canvas represents the number that would go in the corresponding square of the magic square.

The particular magic square Vaze selected to depict in “Ryoanji III” is particularly well balanced each row and column adds up to 34 but each 2 by 2 square also adds up to 34. A nice Fibonacci number!

These are just a few of the interesting works on display at Bridges. I will tell you about some more in my next post!

Susan Happersett