Hong-taek Hwang
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.
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.
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.