# Hongtaek Hwang, Sol Oh* and Ho-gul Park

I enjoy creative activities on the boundary between Math and Art. Sometimes I create artwork with geometrical tube design; at other times I enhance a math visual model to the point where it becomes a piece of art. I have designed “Stars over the Alhambra’s Palace”, “Islamic Tessellation”, and etc. with tubes.

We are developing the spherical versions of tube designs according to the following scheme: First, we observe and analyze the designs of the soccer ball "Telstar" and the "Park's sphere". Second, by mathematical thinking, we get various generalized imagination of the geometrical model of the Telstar. Last, through a series of tube design experiments, we get the creative realities about the mathematically generalized imagination.

For developing our spherical versions of geometrical tube designs, there are basically two types of tube designs. One is expanded horizontally and the other is expanded vertically. Our composition is a natural combination of these two different types of expansions. So it is called “a spherical harmony of horizontality and verticality”.

The spherical version in the figure1 above is a polyframe consisting of 32 units of two types which are horizontally expanded tube designs. On the other hand, the spherical version in the figure2 is a polyframe consisting of 32 units of two types which are vertically expanded tube designs. Moreover, the polyframe "a spherical harmony of horizontality and verticality" mentioned above is a natural combination of the polyframes in figure1 and figure2. Figure3 is another view of the spherical harmony of horizontality and verticality above. Figure4 emphasizes interior of the spherical harmony of horizontality and verticality in the red color.