Near-miss Johnson solid
In geometry, a near-miss Johnson solid is a strictly convex polyhedron whose faces are close to being regular polygons but some or all of which are not precisely regular. Thus, it fails to meet the definition of a Johnson solid, a polyhedron whose faces are all regular, though it "can often be physically constructed without noticing the discrepancy" between its regular and irregular faces. The precise number of near misses depends on how closely the faces of such a polyhedron are required to approximate regular polygons. Some high symmetry near-misses are also symmetrohedra with some perfect regular polygon faces.
Some failed Johnson solid candidates have coplanar faces. These polyhedra can be perturbed to become convex with faces that are arbitrarily close to regular polygons. These cases use 4.4.4.4 vertex figures of the square tiling, 3.3.3.3.3.3 vertex figure of the triangular tiling, as well as 60 degree rhombi divided double equilateral triangle faces, or a 60 degree trapezoid as three equilateral triangles.
Examples: 3.3.3.3.3.3
Rhombic prism
Gyroelongated trigonal pyramid
Triangulated monorectified tetrahedron
Tetratetrahedron, Triangulated tetrahedron
Augmented triangular cupola
Triangulated truncated triangular bipyramid
Hexagonal antiprism,
Gyroelongated hexagonal pyramid
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