Polyhedra with Folded Regular Heptagons

Marcel Tünnissen
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 183–190


It seems that polyhedra with regular heptagons are hard to find if the prism-based polyhedra are excluded. To be able to find attractive polyhedra that can be used for artwork it is argued to release the flatness constraint, which requires planar faces. If the regular heptagons do not need to be flat, they are allowed to be folded. Then they are orbited and holes are filled by triangles. One computer program was developed to model this and another to search for special positions. Some examples of the special case, for which the polyhedron only consists of (folded) heptagons, are shown. These were built out of Chromolux paper.