In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not a uniform polyhedron. There are 92 such solids:

  • 48 composed of the elementary pyramids, cupolas, and rotundas assembled in various ways together with prisms and antiprisms;
  • 35 formed by modifying uniform polyhedra, by augmenting with primitives, diminishing, or gyrating; and
  • 9 which are not derived from "cut-and-paste" manipulations of uniform solids.

Definition and background

A convex polyhedron is the convex hull of a finite set of points in 3-dimensional space, not all in a plane. Its boundary is a finite union of polygons, no two in the same plane; those polygons are called the faces. A Johnson solid is a convex polyhedron

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  • Paper Models of Polyhedra Many links
  • Johnson Solids by George W. Hart.
  • Visual Polyhedra, with 3D models and data for all 92 solids, by David I. McCooey.
  • Images of all 92 solids, categorized, on one page
  • VRML models of Johnson Solids by Jim McNeill
  • VRML models of Johnson Solids by Vladimir Bulatov
  • CRF polychora discovery project attempts to discover CRF polychora (Convex 4-dimensional polytopes with Regular polygons as 2-dimensional Faces), a generalization of the Johnson solids to 4-dimensional space
  • https://levskaya.github.io/polyhedronisme/ a generator of polyhedrons and Conway operations applied to them, including Johnson solids.