Puzzle: use each of the edgelengths 1., 1.10487, 1.22074, 1.34877, 1.49022, 1.6465, 1.81917, 2.00995, 2.22074, 2.45364 a single time to make a polyhedral graph. These values are powers 0 to 9 of the second real root of x^8-x^2-1. So far, I've found 4 solutions for polyhedral graphs made from consecutive power distances. I posted pictures at https://math.stackexchange.com/questions/2592534/polyhedral-graphs-from-cons... You won't believe the fourth polynomial! --Ed Pegg Jr