# Hongtaek Hwang & Sunah Kim

It is well known that the truncated icosahedron(TI) originated from the ancient Greek's philosopher Plato's cosmic imagination based on mathematics. In author's research papers, we had been figured out that the essential components of the truncated icosahedron are twelve pentagons. Hence, for a given regular pentagonal shape(RPS), it is possible for us to image a creative real extension of sphere shape derived from the TI by applying the TI formation scheme. Eventually, through a series of geometric tube design experiments, we can establish the creative real extension mentioned above. We define this real extension by "the Archimedes star with respect to the RPS". Each usual sphere will be a clear example of the Archimedes stars.

In the geometric tube design, there are three kinds of basic expansion methods such as horizontal, skewed and vertical expansion which connect given line segments with physical elasticity.

It is well known that icosahedron is one of Plato’s five solids that symbolizes water. Moreover, it is also a regular pentagonal shape of skewed expansion. So, we can try to create the Archimedes skewed star with respect to the icosahedron. In all, we have established the desired creation succefully. We name the creation "Plato's water star".