Polyedergarten: A German Website's Paper Models of Polyhedra

A website called Polyedergarten, recently highlighted on Hacker News, presents an extensive collection of paper models depicting uniform and other polyhedra, according to the site itself at polyedergarten.de.

According to the site, all of the polyhedra on display are constructed from ordinary typewriter paper, with finished models ranging from roughly 7 to 40 centimeters in diameter. The models are built layer by layer from the inside out, with individual pieces cut by hand using knives and scissors and then assembled with glue. The site notes that the arrangement of the models on the page is largely arbitrary and unsystematic, rather than organized by any particular classification scheme.

Names and "w-numbers" assigned to the models, such as w85 for the quasirhombicuboctahedron, are drawn from Magnus Wenninger's reference book "Polyhedron Models." For nearly every model, the site also lists the type and number of faces.

Beyond the paper models, Polyedergarten functions as a much broader repository of geometric material. Its pages include facetings with regular polygons and crossed quadrilaterals, augmentations of uniform polyhedra, intersecting cylinders, and a section crediting Richard Klitzing's facetings. The site also features named constructions such as the Inverted Snub Dodecadodecahedron, two forms described as "Noble Polyhedra," and the Great Snub Dodecicosidodecahedron.

The broader site extends well past polyhedra into general geometry, according to its own description. It includes notes on polygons and meshes, points, lines and planes, circles, cylinders and spheres, as well as coordinate transformations and map projections. Additional sections cover texture tiling, aperiodic tilings such as Penrose and Pinwheel tiles, contouring algorithms, four-dimensional geometry, and a wide array of mathematical surfaces and curves — from tori and Möbius strips to minimal surfaces, spirals and classical plane curves like the cardioid and astroid.

The site, whose author is not named in the material reviewed, presents itself as a personal, long-running documentation project rather than an institutional or commercial resource. It intersperses its technical content with quotations from figures including Galileo, Albert Einstein, William Blake and Lewis Carroll.

This account is based on text drawn directly from the Polyedergarten website. Readers interested in specific figures, construction techniques or mathematical claims made on the site are encouraged to consult the original source directly at polyedergarten.de before relying on further detail.