Double Layered Polyhedra

Rinus Roelofs ()
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Rinus Roelofs: Independent Sculptor

Chapter 30 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 879-959 from Springer

Abstract: Abstract In their book “La Divina Proportione,” Luca Pacioli and Leonardo da Vinci described and illustrated an operation which you can apply to a polyhedron, called Elevation. Starting from Pacioli’s basic idea, resulting in a second layer around a polyhedral shape, we can develop this idea further towards entwined double layer structures. Some of them are single objects; others appear to be compounds. With the introduction of Elevation by Luca Pacioli and Leonardo da Vinci, the interesting field of double layer structures has been opened. Inspired by Albrecht Dürer, who was the first person to publish folans of the Platonic solids and also some of the Archimedean solids, I investigated the possibility of making folding plans for double polyhedra. For some of the Platonic double layer polyhedra single sheet folding plans can be made. In my opinion, it is important to have real physical models of this group of objects because physical models help to understand the complex structure of these double layered polyhedra. Therefore I developed more ways to create these models. One of those techniques of creating models of double layered polyhedra, based on weaving, is explained here.

Keywords: Polyhedra; Elevation; Folding plans; Models; Leonardo da Vinci; Luca Pacioli; Albrecht Dürer; Branko Grünbaum; Double polyhedra; Knots; Zonohedra; Weaving (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_23

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DOI: 10.1007/978-3-319-57072-3_23

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