Add Johnson solids

Test-problems.md

@@ -113,6 +113,33 @@ Place five unit spheres tangent to each other so that their centers form either
 
 One might reasonably hope that solving this problem will provide a solution of the original Frugal Firepower problem. The idea is that a box that solves the original problem should have “maximal contact” with the spheres, and should therefore be determined by its tangencies with the spheres.
 
+### Johnson solid
+
+#### Statement
+
+Choose a Johnson solid. Assemble it and confirm that it's rigid.
+
+#### Notes
+
+There are various ways to represent the solid and to constrain the faces to be regular. Here's a way that has the advantage of requiring only point–point distance, point–sphere incidence, and curvature constraints.
+
+- For each vertex, create a point.
+- For each edge, add a unit distance constraint between vertices.
+- Constrain the faces to be planar. For each face with more than three vertices:
+  - Create a plane—a sphere whose curvature is constrained to be zero.
+  - Constrain each vertex of the face to lie on the plane.
+- Constrain the faces to be regular. For each face with more than three vertices:
+  - Triangulate the face.
+  - For each triangulation diagonal, add a distance constraint to enforce the desired length.
+
+[Nets for the Johnson solids](https://archive.lib.msu.edu/crcmath/math/math/j/j057.htm) might help with assembly. Here are some interesting Johnson solids with relatively low vertex, edge, and face counts:
+
+- Triangular cupola (J3)
+- Triangular dipyramid (J12)
+- Gyrobifastigium (J26)
+- Tridiminished icosahedron (J63)
+- Snub disphenoid (J84)
+
 ### Ring of polyhedra
 
 #### Source