# Friedhelm Kürpig

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.

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.