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  "body": "\n## Description\n\nA *Johnson solid* is a strictly convex polyhedron whose faces are all [[regular polygons|01KJJ9A400]].\nIt must not be a [[Platonic solid|017E5PRS1Q]], an Archimedean solid, a prism or an antiprism.\nStrictly convex means that no two adjacent faces lie in a common plane.\nThere are exactly $92$ Johnson solids.\n\nExample: the square pyramid with a unit square base and four equilateral triangles is a Johnson solid.\nThe apex lies above the centre of the base at height $h$ with $h^2 + (\\sqrt2/2)^2 = 1$, so $h = \\sqrt2/2$, and all eight edges have length $1$.\nIts faces are regular, but its apex lies on $4$ edges while each base vertex lies on $3$.\nSo it is not vertex-transitive, hence not Platonic or Archimedean, and it is not a prism or an antiprism either.\n\n## Remarks\n\nThe excluded families are the convex [[uniform polyhedra|BZXHGNGQAX]], whose symmetries act transitively on vertices.\nSo the Johnson solids are exactly the strictly convex polyhedra with regular faces that are not vertex-transitive.\nNorman Johnson published the list of $92$ in 1966, and Victor Zalgaller proved that the list is complete.\nOther examples are the pentagonal pyramid, the triangular cupola and the elongated square bipyramid.\n\n## Explanations\n\n### L1 human\n\nTake regular polygons, such as equilateral triangles, squares and regular pentagons, and glue them into a convex solid.\nIf every corner looks the same, the result is a Platonic solid, an Archimedean solid, a prism or an antiprism.\nThe Johnson solids are all the other ones, where some corners differ, and there are exactly $92$ of them.\nA pyramid with a square base and four equilateral sides is the simplest example.\n",
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