The Generation of Hypersymmetrics
The graphical artwork of Jens W. Beyrich
originally consists of hexagonal elements
–“stars”– decomposed into six segments,
that differ by their colour arrangements
(or shape) and are fitted in a structured,
With the combination of three colours unevenly applied – three segments show one colour, two segments a second colour and one segment a third colour –, a group of 10 stars with different colour arrangements can be obtained. All colours may be exchanged among themselves, generating a set of 60 different stars.
The grid may be for example orthogonal, as shown in Star Field, hexagonal, circular or even spherical. The number of places in the grid is equal to (or a multiple of) the number of stars in a set. No rules applied, any star may be fitted in a chosen grid at random. For the first star 60 places are available, for the next remain 59, until the last has to be fitted in the last place left. The total of placing solutions is 60 × 59 × ... × 1 = 60! = 8.32 × 10⁸¹ - an 8 followed by 81 zeros.
Since all stars show no rotation symmetry, they can be fitted at any place in six different positions. As the individual rotation position of any star is independent from any other, this leads for each placing solution to a total of rotation possibilities of 6 × 6 × 6 ... × 6 = 6⁶⁰ = 4.89 × 10⁴⁶. Placing and rotating being independent, a set of stars can be arranged in any grid in 60! × 6⁶⁰ = 4.066772 × 10¹²⁸ different ways, a 4 followed by 128 zeros. The number of atoms the earth consists of is about 10⁵⁰, the atoms in the known universe are estimated to be around 10⁸⁰.
The hypersymmetric approach underlying all artwork, both graphic and sculptural, is the conscious playing with interwoven symmetries. Despite all stars being different and showing no rotation symmetry, advanced choreography allows the simultaneous presence of combined rotation, point or open book symmetries with partial inversions.
The more than astronomic base of possible solutions, respective rules applied, may boil down to comparably few, sometimes just one or no solution at all.