Star Sphere

The Icon

The original allegoric meaning of stars on flags, such as for instance those on the US flag or later the European Union, has been to symbolise the “Unity of Unequal”. For this reason, equally looking stars, monochrome and of equal size, with homomorph structure, that is five pointed, were used: the top point stands for the head, the middle two for arms, the lower two for feet, in accordance to Leonardo's famous drawing of the Vitruvian man, standing simultaneously in a circle and a square.
The full set of sixty different triple coloured six pointed stars, similar to the preceding polyhedral sculpture, can be distributed evenly on the sphere's surface. There is only one perpetuating grid, a structured web, fitting in all stars. The ever changing individual arrangements of colours of the individual stars contrast pleasingly to the grid's apparent regular aspect.
Furthermore, each six pointed star is an integrated part of the structured web, communicating by touching with five of its points the respective neighbour stars, leaving only one point disconnected. By applying the chosen set of rules of symmetries, including a rule of reciprocity relative to its equator, the stars present the sphere's opposing hemispheres in mutual accordance, no matter the orientation. A regular, pole free grid around a sphere as a symbol of a global web, making use of the complete set of different stars as a symbol of integration of the individual, communication and ever complementary hemispheres, today's spirit of global thinking.
The Star Sphere is easily recognisable as an unprecedented sculpture, possibly a future icon, similar to Robert Indiana’s “Love” and “Hope” sculptures in the 60s.

A Numerical Approach

The total possible arrangements of a set of 60 individually differentiable and dissymmetric stars, as previously described, is determined by the short mathematical formula 59! × 6⁶⁰ and leads to the breath- taking number of 6.8 × 10¹²⁶, a six followed by 8 and further 125 zeros.
For comparison, the number of atoms in the known universe is estimated to be around 10⁶⁰ - this is 46 zeros less!
By application of specific rules of symmetry the stars on the sphere should fulfil, the number of possible arrangements decreases at a similar fantastic speed. Just regrouping the set of sixty stars in 20 preselected triples, determined by certain intrinsic rules of symmetry among the stars themselves, does not only generate certain optical harmony, but lowers the number of possible arrangements to 19! × 3¹⁹ = 1.4 × 10²⁶. For comparison, in the number of Avogadro, the number of atoms in 1 gram of hydrogen is 6.022 × 10²³.
The rule of reciprocity relative to its equator further reduces the number of arrangements to 9! x 6 9 = 3.65 × 10¹², three point six trillions.
A final requirement, all stars should “communicate and exchange” by touching the respective points of their neighbour stars only if colours are different (i.e. never two touching points show the same colour), the number of possible solutions goes further down dramatically, though it is only an estimate, to the level of thousands. Thus it suggests that it is more likely to find life on another planet in the universe than a solution respecting the portfolio of rules of symmetry set among the total of possible solutions…

Engineer's Finest

Designing, drawing and producing perfect geometric bodies, such as polyhedrons or spheres, in all cultures and periods of history has fascinated artists, scientists and craftsmen. Let’s refer to the ancient stone spheres of Costa Rica, originated most probably about 2000 years ago, or to Leonardo's drawings of perfectly symmetric solids, the interest for regular geometric bodies in the Renaissance (De Divina Proportione by Luca Pacioli), until the late artwork of M.C. Escher.
Only most recent programmable high- precision milling machines with specifically adopted software turned out to be able to cut the components required for the production of the Star Sphere. Twenty spherical triangle parts, with cut off spherical cavities are assembled with a tolerance of a hundredth millimetre. The star inlays, as well as the sphere parts, are anodised to ensure a long lasting vividly coloured metallic appearance. Every single lozenge the stars are decomposed into shows a spherical bending to precisely fit into the sphere's cavities.

Star Sphere

The Icon

Star Sphere

A Numerical Approach

Star Sphere

Engineer's Finest

Star Sphere

The project