We enjoy creative activities on the boundary between mathematics and art. Sometimes we create artwork by using geometric tube design.
The truncated icosahedron is one of the Archimedean solids, generalizations of Plato's regular solids. The soccer ball "Telstar" and the nano technology molecule model "Fullerene" are instantiations of it.
For a given regular pentagonal shape(RPS*), it is possible for us to image a creative transformation of the soccer ball Telstar derived from the truncated icosahedron(TI) by applying the TI formation scheme. Eventually, through a series of geometric tube design experiments, we arrive at a model called the Archimedean star with respect to the RPS*.
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. There are also three kinds of Archimedes stars such as Archimedes horizontal, skewed and vertical stars.
In particular, we apply the horizontal expansion of geometric tube design to design an advanced regular pentagonal shape * by using certain combinations of 72 degree only. Then, we can establish a beautiful Archimedes horizontal star with respect to the advanced regular pentagonal shape*. Since the shape of every Archimedes horizontal star is a kind of usual sphere, we call this beautiful sphere H star.