Near-miss Johnson solid
In geometry, a near-miss Johnson solid is a strictly convex polyhedron in which the faces are close to being regular polygons but in which some or all of the faces are not precisely regular. They generalize the Johnson solids, polyhedra in which all faces are regular, and "can often be physically constructed without noticing the discrepancy" between their 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.
|Truncated triakis tetrahedron||4 (5.5.5)
|Tetrated dodecahedron||4 (5.5.5)
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 22.214.171.124 vertex figures of the square tiling, 126.96.36.199.3.3 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.
- Platonic solid
- Semiregular polyhedron
- Johnson solids
- Geodesic dome
- Truncated rhombic dodecahedron
- Kaplan, Craig S.; Hart, George W. (2001), "Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons", Bridges: Mathematical Connections in Art, Music and Science.