Johannes Wallner,c Helmut Pottmanna,d

Abstract. This paper builds on recent progress in computing with geometric con-straints, which is particularly relevant to architectural geometry. Not only do var-ious kinds of meshes with additional properties (like planar faces, or with equilib-rium forces in their edges) become available for interactive geometric modeling, but so do other arrangements of geometric primitives, like honeycomb structures. The latter constitute an important class of geometric objects, with relations to “Lobel” meshes, and to freeform polyhedral patterns. Such patterns are particularly inter-esting and pose research problems which go beyond what is known for meshes, e.g. with regard to their computing, their flexibility, and the assessment of their fairness.