# 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.

Icosahedron orbited by a concentric Hamilton cycle on an icosidodecahedron with a common vertical axis, but without its own rotational symmetry. Each Hamilton cycle is a closed chain of edges which has to be constructed as a rigid entity. Two half edges are therefore combined to form corner units and then joined at the centre of the edges. This is only possible by means of invisible constructions inserted into the interior of the tubing. The sections of tube are mitred and glued to a precisely lasered angle plate. The corner units are connected by cylinders with slots at each end and inserted into the tubing. These slots are twisted at the angle of the adjacent polyhedral surfaces thus incorporating the ends of the angle plates.

Two different Hamilton cycles with threefold symmetry on a
truncated icosahedron.

Each Hamilton cycle on regular and semi-regular solids divides the
surface into two sections. If one is rendered visible in material
form, and the other is regarded as an imaginary supplement of the
whole, then the border between the two sections represents the
given cycle. To trace the complete cycles in this case, one must
imagine either the upper or lower hexagon as non-existent.