Hong-taek Hwang

Emeritus Professor
Dept. of Applied Mathematics, Kumoh National Institute of Tcchnology
Gumi, South Korea

Unlike other regular polygons, regular pentagons have a special property that is advantageous for a sphere-like surface composition. Therefore, I am particularly interested in research that makes creative changes to the dodecahedron, a polyhedron consisting of only regular pentagons. Because I think that these efforts will be of great help in creating mathematically designed art.

We know that unit of each regular pentagon is certain line segment and is rotational invariant of period 72 degree. On the other hand, there exists a special line connection which consists of two line segments of same length where the angle between the two line segments is 116. 57 degree.

42 x 42 x 42 cm
digital image

We define a H-Pentagon by a geometrical figure whose unit is a special line connection mentioned above and is rotational invariant of period 72 degree

Note that regular pentagon and H-Pentagon have the same mathematical essence. However, the former is two dimensional figure but the latter is three dimensional.

We know that dodecahedron(so called Plato's universe) is the unique solid which consists of twelve unit(regular pentagon)s.

In the research modeling, we figured out that the special angle 116.57 degree between two segments of same length yields the unique solid which consists of twelve unit(H-pentagon)s. We call this unique solid H-universe.

A combination of transformations of the Plato universe
360 x 360 x 360 cm
digital image

We can build twelves same vertical halls on twelves H - pentagons in the H-universe respectively. Hence there exists a natural combination of these twelves halls and the H-universe. We call this natural combination the H - Big Bang. The digital image in the figure above is a harmony of certain modifications of the Plato's universe and the H - Big Bang. We will use it an excellent sketch for the construction of certain great mathematical sculpture.