# 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,
regular grid.

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.