[math-fun] Rotundancy

Mathematica likes to tabulate polyhedra with their centroid at the origin, and unit edges. An interesting exception is the Johnson solid In[459]:= ToRadicals[PolyhedronData["ElongatedPentagonalRotunda", "Centroid"]] Out[459]= {0, 0, (-3735 + 1689 Sqrt[5] - Sqrt[2 (1449845 - 3240379/Sqrt[5])])/13928} (Elongated = glued to a prism with square faces.) Even more interesting is how close this is to the origin: In[460]:= N@% Out[460]= {0., 0., 0.0003022667749277455} So it just barely won't stand on a square face. --rwg You could use one as a carpenter's level. It must tip over, and again when rotated 180º.