Meissner's mysterious bodies
Precisely a century ago, Ernst Meissner introduced the special convex bodies of constant width, based on a regular tetrahedron, that are now named after him. It is a well-known and still unsolved conjecture that the Meissner bodies have the smallest volume among all three-dimensional convex bodies of the same constant width. This well-written and nicely illustrated popular survey article describes the Meissner bodies, presents their history, and explains some recently established necessary conditions for the solution bodies of the mentioned extremal problem. The article concludes with a short biography of Ernst Meissner. It has a useful list of references.
scientific article; zbMATH DE number 5971474
scientific article