30 Mar
2014
30 Mar
'14
7:32 p.m.
This video raises the question: what are all the "circle crystals," i.e., 3D "lattices" of identical circles with each contacting n equally spaced neighbors, all with the same twist angle (as seen along a line connecting two centers and the point of contact). (Roughly: the symmetry group acts transitively on the circles.) https://www.youtube.com/watch?v=_XfwgngPrhE Three 2D cases, one 1D continuous family, and two interesting 3D cases are shown. Are there any other discrete examples I missed? Is there a succinct proof of completeness? Are there others that deserve to be physically constructed? George http://georgehart.com/