Hongtaek Hwang

MathArtist, Professor & Director
Dept. of Applied Mathematics & Agency of Hands-On Science Class, Kumoh National Institute of Technology
Gumi, South Korea

It is well known that the truncated icosahedron(TI) originated from the ancient Greek's philosopher Plato's cosmic imagination based on mathematics. Buckminster Fuller's geodesic structure, the soccer ball "Telstar" and Nano technology molecule model "Fullerene" are realities of it.

For a given regular pentagonal shape(RPS), it is possible for us to image a creative extention of sphere pattern derived from the TI by applying the TI formation scheme. Eventually, through a series of geometric tube design experiments, we can establish a geometric reality of the creative spherical pattern image. We call this reality the Archimedean star with respect to the RPS. Each usual sphere will be a clear example of the Archimedean stars.

The Archimedean Star Flower
Geometric Tube Design

Icosahedron as one of Platon’s four ideal geometric components which form universe also is a regular polyhedron to symbolize water. The composition "Archimedean star flower" must be the one that originates from Plato's cosmic imagination based on mathematics. In fact, it is a fractal combination of certain Archimedean skewed stars which are of double form and also an abstract transformation derived from the design of Fullerene and Telstar.

Archimedean Star Box
Geometric Tube Design

It is an Archimedean Skewed Star of Single Form

Acknowledgement : These art works are research results which had been established under the professor research year policy of Kumoh national institute of technology.