# Friedhelm Kürpig

Professor of Descriptive Geometry (retired)

University of Fine Arts Hamburg

Aachen, Germany

For the author, geometry has not lost anything of its fascination even after over fifty years of intense engagement with the subject. As an architect, he finds it a never-failing source of innovation and a symbol of eternal beauty. In his capacity as Professor of Descriptive Geometry at the University of Fine Arts in Hamburg, his most important secondary activity lay in the development and production of educational models as visualizations of geometric laws. These models were generally acquired by Technical Universities as learning material for lectures and seminars. Over the years the emphasis of his work has changed somewhat, and today he prefers to focus on the aesthetic rather than on the didactic aspects of his objects.

Pentagonal dodecahedron without casing

24 x 20 x 22 cm

Stainless steel sheet, Thickness 2,5 mm

2020

To determine the form of a dodecahedron circumscribed around a given cube, we start with the 8 vertices of the cube, which also act as the dodecahedron’s vertices. For the 12 missing vertices, we need to define the corners of 3 congruent interlocking rectangles incorporated concentrically into the cube, parallel to its planes. To calculate the length of these rectangles, we multiply the length of the cube edge by the numerical proportion of the golden section (phi=1,618...); for their width, we multiply the latter by its reciprocal value. This rectangle can be divided into a golden rectangle and a square or into 2 squares and a smaller golden rectangle. It is the basis of dodecahedral structure and formed the basic concept of this artwork.