Renate Quehenberger

Art researcher
Independent
Vienna

I am a captive of Plato's Ideal World

-- focusing on the visualization of higher-dimensional spaces and their physical significances I am exploring different geometries and their application through the history of art and science.

Currently I am editing the book <Quantum Cinema - a digital vision> on the visualization of quantum phenomena by means of digital arts.

Besides pursuing my thesis in philosophy 'On the Hermeneutics of the Penrose Pattern' I'm promoting my contribution to mathematics: the 3D representation of the Penrose Kites and Darts tiling through various publications, screenings and exhibitions in the art and science contexts.


Epitahedron (E±)
35 x 50 x 45 cm
Acrylic sheets, printed
2015

Epitahedra are the 3D representation of the Penrose Kites and Darts tiling.

The volume of the convex epitahedron E+ (E "plus") demeans 1/6 (0,666667) and the concave E- (E "minus") φ /6 (0,1030057).

Thus the volumes of E+ and E- are in the Golden Ratio as well as the lengths of the edges. the volumes of the concave epitahedron (E-) and the convex (E+) and both together (EE ) are conform to the golden ratio:

E- : E+ = E+ : EE = φ (≅ 1.618).

Dividing EE into E+ and E- therefore means dividing space in the golden ratio

analogous to the tessellation of the plane by means of Penrose patterns.