Main Index Page

Last updated 27/7/2025

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Note that this page only shows early instances of the use of this technique.

There is a separate page about The Additional Froebelian Occupation of Constructing Polyhedra from Irregular Nets after the death of Froebel in 1852.

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1509

According to Max Stech in his book 'Dürers Gestaltlehre der Mathematik und der bildenden Künste (Dürer's Gestalt Theory of Mathematics and the Fine Arts), published by Halle an der Saale in 1948, a 1509 Venetian edition of 'Divina Proportione' by Luca Pacioli and illustrated by Leonardo da Vinci contains a drawing showing the foldable net of a regular dodecahedron. (Information from 'A History of Folding in Mathematics by Michael Freedman, published by Birkhauser in 2018.) I have not been able to verify this information.

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Charles de Bovelles (variously also known as Carolus or Bovillus) book 'Libellus de Matematicis Corporibus', published in 1510, included drawings of polyhedral nets for an icosahedron ( in three parts) and a fifteen sided solid constructed by adding pyramids to the pentagonal faces of a pentagonal prism. (Information from 'A History of Folding in Mathematics by Michael Freedman, published by Birkhauser in 2018.) I been not able to verify this information.

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1525

The fourth book of Albrecht Durer's 'Underweysung der Messung', published in 1525, contained foldable polyhedral nets for the five platonic solids, the truncated tetrahedron, the cuboctahedron, the truncated octahedron, the truncated cube, the rhombicuboctahedron, the truncated cuboctahedron, the snub cube and an eighteen sided solid made by adding pyramids to both hexagonal faces of a hexagonal prism.

A revised edition, published in 1538, also included nets for the truncated icosahedron and the icosidodecahedron. (Information from 'A History of Folding in Mathematics by Michael Freedman, published by Birkhauser in 2018.)

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Cut and Fold Polyhedral Nets also appear in:

1636

Deliciae physico mathematicae oder mathematische und philosophische Erquickstunden' by Daniel Schwenter, which was published in Nürnberg in 1636, contained a net for the Rhombic Dodecahedron and a half net for the Triacontahedron.

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1651

Volume 2 of 'Deliciae physico mathematicae' written by Georg Phillip Harsdorffer, and published in 1651 gave cut and fold nets for the cube, octahedron and dodecahedron.

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1653

Volume 3 of 'Deliciae physico mathematicae' written by Georg Phillip Harsdorffer, and published in 1653 gave a net for the rhombicuboctahedron (although the net is incorrect as it is ten segments, rather than just eight, in height).

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