Add near-miss Johnson solids

Test-problems.md

@@ -285,6 +285,19 @@ These problems impose various kinds of *soft constraints* on top of the *hard co
 
 “David Seppala-Holtzman of St. Joseph’s College New York gives us the following problem. A customer orders five identical perfectly spherical cannonballs from Adderley’s Cannonball Emporium, and it’s your job to pack them for shipping. The Emporium ships only in rectangular boxes but can construct such boxes with any desired dimensions. You have a choice of packing the cannonballs so that their centers form a square pyramid or two triangular pyramids, as in figure 1 [see source], but you can orient the arrangements however you like inside the box.  The shipping cost will be proportional to the sum of the length, width, and height of the box.  In **Frugal Firepower**, determine which arrangement allows you to minimize the shipping cost.”
 
+### Near-miss Johnson solid
+
+#### Statement
+
+Choose a near-miss Johnson solid and a measure of distortion. Look for a minimal-distortion realization of the solid. You could include some hard constraints by restricting distortion to faces below a certain number of sides, like Jim McNeill does for near-miss [Johnson solids](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/jsmn.htm) and [acrohedra](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/554.htm).
+
+#### Notes
+
+Some distortion measures include:
+
+- An $\ell^p$ norm on the vector of lengths of edges and face diagonals.
+  - The $\ell^1$ norm might be equivalent to the $E + P$ measure [used by Jim McNeill](https://www.orchidpalms.com/polyhedra/stress_maps.htm#Distortion).
+
 ## Algebraic relations
 
 ### Circular string art