Well I didn't get to it last night, but I did get to it today. The following page contains coordination sequences for all of the Platonic, Archimedean, and Catalan solids. It also contains links in the left column to interactive images (if you have a mouse, you can click and drag to manually rotate them, or you can let them spin by themselves): https://www.karzes.com/polyhedra/cs_info.html Tom Tom Karzes writes:
I'll look at this later tonight (it's early afternoon where I am). I have all the data, but I'll need to massage it a little to get it into the form I need, and I'll need to display the results in a satisfying manner. But once I have it set up, handling all of the cases will be no harder than handling one of them.
I hadn't really thought about the infinite (planar) cases, but with a bit more work I can probably do something for those as well. At the moment, I handle them as toroidal tilings, with a horizontal and vertical replication factor.
Tom
Neil Sloane writes:
Dear Tom Karzes , For those polyhedra that you mention, some of the coordination sequences are too short (like 1 3 3 1 for the cube) or too similar to other sequences; and some of the others, the easier ones, I have done by hand, but I haven't done them all - and I would certainly like to get them.
Maybe the simplest way to do this would be for you to do them all (more-or-less! - if there are infinite series like the prisms then just do the first handful), and send them to me, and I'll make the decision about which ones are too short, etc., and then I will add the ones I don't have to the OEIS (giving you credit of course)
I'm glad you suggested this - it is something that has needed doing for a long time.
And don't feel that you need to restrict this to the classical solids that you mentioned. Non-convex solids are also worth doing, even solids with holes.
That is opening up a large can of worms, of course - so if other folks want to help then by all means join in.
I remember that many years ago Tom Duff (on this list) had a catalog at Bell Labs of a great many solids and their properties. I still have the TM somewhere.
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Mon, Jan 6, 2020 at 3:22 PM Tom Karzes <karzes@sonic.net> wrote:
Neil, do you have coordination sequences for all of the Platonic/Archimedean/Catalan solids? Those seem like the most fundamental ones for polyhedra. I could probably generate them without too much trouble if needed.
Tom