Add the 5-5-4 acrohedron problem

Test-problems.md

@@ -140,6 +140,26 @@ There are various ways to represent the solid and to constrain the faces to be r
 - Tridiminished icosahedron (J63)
 - Snub disphenoid (J84)
 
+### 5-5-4 acrohedron
+
+#### Source
+
+- **Author:** Jim McNeill
+- **Published:** [“Acrohedra”](https://www.orchidpalms.com/polyhedra/acrohedra/acrohedra.html) and [“5-5-4 Near Misses.”](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/554.htm) [Polyhedra](https://www.orchidpalms.com/polyhedra/).
+
+#### Statement
+
+Try to assemble a 5-5-4 acrohedron, which is a polyhedron with the following properties:
+
+- Every face is a regular polygon.
+- There’s some vertex whose neighboring faces are a 5-gon, a 5-gon, and a 4-gon, in that cyclic order.
+
+If the candidate is a [known near miss](https://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/554.htm), confirm that realization fails.
+
+#### Notes
+
+The problem of finding a 5-5-4 acrohedron is open as of June 2025.
+
 ### Ring of polyhedra
 
 #### Source