Geometry and Freeform Architecture

Helmut Pottmann, Johannes Wallner


During the last decade, the geometric aspects of freeform architecture have defined a field of applications which is systematically explored and which conversely serves as inspiration for new mathematical research. Topics relevant to the realization of freeform skins by various means (flat and curved panels, straight and curved members, masonry, etc.) are discussed and the interrelations of those questions with theory, in particular discrete differential geometry and discrete conformal geometry, will be illuminated.

A substantial part of mathematics is inspired by problems which originate outside the field. In this case the outside inspiration from a rather unlikely source, namely architecture. The topic is the unexpected interplay of geometry with the spatial decomposition of freeform architecture into beams, panels, bricks and other physical and virtual building blocks. As it turns out, the mathematical questions which arise in this context proved very attractive, and the mundane objects of building construction apparently are connected to several well-developed mathematical theories, in particular discrete differential geometry.


  • Helmut Pottmann and Johannes Wallner.
    Geometry and freeform architecture.
    In Wolfgang König, editor, Mathematics and Society, pages 131–151. EMS, 2016.

Prof. Dr. Helmut Pottmann   +

Projects: C01
University: TU Wien
E-Mail: pottmann[at]
University: King Abdullah University of Science and Technology
E-Mail: helmut.pottmann[at]

Prof. Dr. Johannes Wallner   +

Projects: C01
University: TU Graz
E-Mail: j.wallner[at]