Net (polyhedron)

[1] An early instance of polyhedral nets appears in the works of Albrecht Dürer, whose 1525 book A Course in the Art of Measurement with Compass and Ruler (Unterweysung der Messung mit dem Zyrkel und Rychtscheyd ) included nets for the Platonic solids and several of the Archimedean solids.

[5] In 2014 Mohammad Ghomi showed that every convex polyhedron admits a net after an affine transformation.

[12] Furthermore, in 2019 Barvinok and Ghomi showed that a generalization of Dürer's conjecture fails for pseudo edges,[13] i.e., a network of geodesics which connect vertices of the polyhedron and form a graph with convex faces.

[15] The spider and the fly problem is a recreational mathematics puzzle which involves finding the shortest path between two points on a cuboid.

The net of the tesseract, the four-dimensional hypercube, is used prominently in a painting by Salvador Dalí, Crucifixion (Corpus Hypercubus) (1954).

[16] The same tesseract net is central to the plot of the short story "—And He Built a Crooked House—" by Robert A.

A net of a regular dodecahedron
The eleven nets of a cube
Four hexagons that, when glued to form a regular octahedron as depicted, produce folds across three of the diagonals of each hexagon. The edges between the hexagons remain unfolded.
Blooming a regular dodecahedron
The Dalí cross , one of the 261 nets of the tesseract