# Heon Jeong Ha and Hongtaek Hwang*

We enjoy creative activities on the boundary between Mathematics and Art. Sometimes we create artwork by using geometric tube design.

It is well known that the truncated icosahedron(TI) originated from the ancient Greek's great philosopher Plato's cosmic imagination based on mathematics. We define the regular pentagonal shape(RPS) by the rotational invariant finite figure in the period of 2π/5 radian. For a given RPS, it is possible for us to image a creative spherical 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 image. We call this reality the Archimedean star with respect to the RPS.

There are three basic expansions, namely horizontal expansion, skewed expansion and vertical expansion of geometric tube design as fundamental methodologies of connecting line segments. And also there are three types of Archimedean stars according to the three basic expansions of the geometric tube design