Near-miss Johnson solid

A near-miss Johnson solid is a polyhedron that visually approximates a Johnson solid, but which does not meet all of the requirements to be one. It can have slightly irregular faces, usually close enough to regular that one can make a physical model with regular faces and not notice a problem, by having slightly differing edge lengths and/or internal angles of faces.

Near-miss Johnson solids can be divided into two types:

If all vertices of a near-miss Johnson solid have polyhedral angles measuring less than 2π (if the polygons surrounding those vertices were regular), the polyhedron is considered locally spherical. If a near-miss Johnson solid has any vertices that are planar (if the polygons surrounding those vertices were regular), the polyhedron is considered locally Euclidean.

The Goldberg polyhedra and their dual geodesic polyhedra may also be thought of as locally Euclidean near-miss Johnson solids since they approach the regular hexagonal tiling and the triangular tiling respectively as the number of faces increases.

Unlike Johnson solids which have at most prismatic or antiprismatic symmetry, these near-misses can have high degrees of symmetry.