A symmetrist's comments to John Hiigli's "Select Paintings"

The reader can follow the evolution of John Hiigli's artistic development from the early years up to now, like in an unusual biography of an artist. His documentation of over fifty large-scale artworks allow us an insight not only into his workshop, but also into the creating mind of the artist. Rare that artists share these „secrets” with the admirers of their art. However, his comments facilitate an understanding of his works. This statement holds especially for the mathematically less sophisticated art-lovers.

One could think that polyhedra are such simple geometric objects that their mathematics has probably been disclosed centuries ago, and their simplicity does not leave space for the artistic imagination. Neither of the two is the case. Many secrets of the regular, semi-regular, semi-semi-regular, ... polyhedra have been discovered in recent decades and there are so many others waiting for disclosure. All new and all mathematically less described properties of these bodies open the floor for artistic imagination, representation, that may then inspire further the minds of mathematicians.

In short, the art of J.A. Hiigli lies in a domain where science and art intersect each other. The geometry of polyhedra interested scientists in their relation to the perfect crystals for centuries. Perfect crystals are those that show the symmetry properties of the 230 crsytallographic groups (in algebraic sense), established and systemized by the end of the nineteenth century. Their application in the material sciences justified this selection.

Nevertheless, the class of symmetry properties of the polyhedra includes more features than those appearing in the „classical” crystals. It is worth mentioning only the five perfect Platonic polyhedra whose symmetries include several such that never appear in crystals. E.g., one cannot build a spacefilling crystal made of dodecahedra, and we could continue the listing.

J.A. Hiigli has obtained a primary and long lasting inspiration from R.B. Fuller's Synergetics. Especially the use of IVM (Isometric Vector Matrix) as a method shaped him during his artistic career. He applied the same basic symmetry transformations in his representations which had appeared already in crystallography (namely, mirror reflection, rotation, inversion, translation/repetition), but he extended them. He did not insist on 3-, 4- and 6-fold rotations only. Moreover he extended the set of symmetry operations that have appeared in crystallograpyhy through the use of such symmetry properties as similitude (which led him to the world of self-similar fractals) and beyond the geometric properties, with the permutation of colours (both transparent and opaque). His drawings combined with the color representation reveal the unique and personal character of his artworks and distinguish them from simple geometric designs made by geometers and architects. It is enough to have a short blick to most of his paintings to see how art was born by the systematic use of colors from geometry. The use of colors represents translational symmetry in the world of light frequencies, while the mixing of transparent colors over each other remind us of the composition of sound frequencies in musical artworks. The extension of the simple geometric forms of polyhedra by multiple-fold rotations opened for him an infinite kaleidoscopic world towards the beauty of systematic variation of the chosen basic elements.

Conscious application of symmetries made it possible to show a much richer world of forms and their beauty than nature (crystals) could produce ever. Extension of the artist's palette with new kinds and combination of various symmetries brought always revolutionary changes in artistic representation. Remember only the appearance of different forms of perspective (spatial projection from one, two, three or more vanishing points, aerial perspective), then recall the multiple view points applied by cubism and futurism and the application of real 3D symmetries with the appearance of mobile artworks. Also consider the series of manifestations of geometric art movements of the twentieth century, and the artistic representation of impossible objects and visual illusions. J.A. Hiigli continues these avantguard traditions, remaining in the real world of semi-perfect polyhedra. Important to enjoy by friends both of arts and sciences.

Gyorgy Darvas
Senior research fellow
Institute for Research Organization of the Hungarian Academy of Sciences
Budapest, January 2014