Polyhedra and polytopes27 of 113
Truncation
after Kepler’s Harmonices Mundi, 1619
Slice every corner off a cube and keep slicing. The cut faces, marked in red, grow while the old faces shrink, through the truncated cube to the cuboctahedron, where they balance, then on to the octahedron. The same walk links the dodecahedron to the icosahedron, and the tetrahedron to itself.
each corner → points at s along its edges, 0 ≤ s ≤ ½
On mathcurve.com as Troncature
Variant
Drawn as
In the library
3
Divine ProportionLeonardo da VinciVenice: Paganinus de Paganinus, 1509The Art Institute of Chicago The solid on plate XIII is a cube with its corners cut away, the first step of the walk from cube to octahedron, here with a pyramid raised on each face.
Not yet checkedSuggested by an AI model, 2026-10-08Source
An AI reviewer had doubts, 2026-10-09: The library's entry describes truncation as "Slice every corner off a cube and keep slicing." The plate shows a cube with pyramids raised on its faces, but I cannot see cut corners in the woodcut, and nothing in the evidence translates the caption word "Abscisum", so the corner-cutting part of the note is not borne out.
Melencolia IAlbrecht Dürer1514Metropolitan Museum of Art, New York, NY The stone block on the left is a truncated solid: a rhombohedron stretched along one axis with two opposite corners cut off, now called Dürer’s solid. What exactly it is has been argued since the nineteenth century.
Not yet checkedSuggested by an AI model, 2026-10-08Source
An AI reviewer had doubts, 2026-10-09: The page confirms a debated truncated rhombohedron, and the picture shows that block at left. But it says "The shape of the solid depicted by Dürer is a subject of some academic debate" and dates its earliest cited work to 1900, so nothing there backs the note's claim that the argument began in the nineteenth century.
Melencolia IAlbrecht Dürer (German, 1471–1528)1514Cleveland Museum of Art A second impression of Melencolia I. The stone block on the left is the truncated solid now called Dürer’s solid.
Not yet checkedSuggested by an AI model, 2026-10-08Source
An AI reviewer had doubts, 2026-10-09: The large cut stone block on the left matches the source, which says "This polyhedron is sometimes called Dürer's solid, from its appearance in Albrecht Dürer's 1514 engraving Melencolia I." The Cleveland record gives no impression state, so the note's "second impression" is not borne out, and the block is a truncated rhombohedron, not one of the cube walks in the library's Truncation entry.