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… and the hexagon -pentagon solution was used in the 1966 World Cup footballs (which my grandfather sewed together ;-). John Summerscales. From: Engineers and biologists mechanical design list [mailto:[log in to unmask]] On Behalf Of Steven Vogel Sent: 20 September 2012 16:13 To: [log in to unmask] Subject: Re: Tiling eyes! Hi All, I built a couple of geodesic jungle gyms from EMT conduit, so I got into this business from a different angle. As I understand it, one cannot close up a full sphere or other closed shape with a surface of hexagonal plates. One needs to insert (for a full sphere) twelve pentagons. Put another way, there's an embedded dodecahedron in each geodesic sphere. For a long time I've wondered if that requirement for pentagons drove echinoderms to their pentaradial semisymmetry, which have plenty of outer plates. Steve Vogel ----- Original Message ----- From: "Engineers and biologists mechanical design list" <[log in to unmask]> To: <[log in to unmask]<mailto:[log in to unmask]>> Cc: Sent: Thu, 20 Sep 2012 16:05:33 +0100 Subject: Re: Tiling eyes! HI do they have to be perfect hexagons (which by definition I don't think thay can be anyway)? Why not take the inverse approach and seed your curved surface with points on a triangular lattice and calculate the Voronoi cells, I think (of course without trying) that you would get a nice slightly irregular but useful tiling? cheers Mark Jessell IRD Toulouse