Johnsonveelvlakken

Johnsonveelvlakken, also known as Johnson solids, are a set of 92 convex polyhedra, each face of which is a regular polygon. They are named after Victor Zong, a mathematician who cataloged them in 1966. Unlike the Platonic solids, where all faces are congruent and all vertices are identical, Johnson solids can have different types of regular polygons as their faces, and their vertices do not necessarily have the same arrangement of faces.

The definition of a Johnson solid excludes the 13 Archimedean solids, which also have faces made of regular polygons but are required to have vertex-transitivity, meaning all vertices are identical. The Platonic solids are also excluded as they are a subset of the Archimedean solids. The Johnson solids are characterized by being convex and having only regular polygons as faces.

The smallest Johnson solid is the triangular pyramid (J1), which has four equilateral triangles as its faces. Other examples include the square pyramid (J1), which has a square base and four triangular faces, and the pentagonal pyramid (J2). As the number of faces and vertices increases, the complexity and variety of Johnson solids grow. They can be constructed by augmenting, decrementing, or combining simpler polyhedra, often involving squares, equilateral triangles, and pentagons. Their study is important in geometry and polyhedral combinatorics, providing a rich set of examples that lie between the highly regular Platonic and Archimedean solids and the more general convex polyhedra.