I need to create a pattern for cutting clay so that it can be wrapped around a globe. The twelve gore style is too complex for what I’m doing; I need a greater degree of integrity. I was looking at some of the map shapes here:
but I believe that part of the irregular shape is designed to create uninterrupted depictions of land masses and oceans. If I didn’t care about such things, what would be the simplest 3 or 4 gore/lobe shape to approximate a sphere?
When I’ve had similar problems in crafts projects, I’ve found that the best way to wrap flat pieces around a sphere is the baseball pattern, with just two pieces. I’m not sure if I can describe it, but am I safe in assuming you’ve seen baseballs?
The problem with the tennis ball pattern is that it’s composed of two parts. I need something a bit simpler because these pieces will be small (wrapped around a half to one inch bead) and I’d be making quite a few. The four lobe globe I linked to is good, but I think they warped it a bit just to maintain integrity of land masses. There must be a “basic” version somewhere but hell if I can find it.
I’m not familiar with the term “gore”, but if a tennis ball is “two gore” (as MrDibble asserts) then I’m willing to bet that the unfolded dodecahedron is the “twelve gore” form the OP said was too complicated.
For something that small, I think it’s going to be hard to cut a shape that doesn’t overlap, fall short or need excessive stretching; is there a reason why you can’t just apply a few small, separate pieces of clay and work them together to cover the bead?
If accuracy really is a big issue, then I would suggest doing the above, then cutting it off (probably a crosscut starting at one end and extending three quarters of the way to the other) and flattening it to make a pattern.
Given the malleability of the material, the simplest shape would probably be a very long, thin strip - wrap it around the form in a spiral and cut off any excess.
I assumed what he meany by “twelve gore” was that orange-peel-segmented shape that I usually see globes dissected into. The problem with that shape and the “baseball/tennis ball” “Gores” is that they assume the surface can be distorted to cover the shape (otherwise the baseball/tennisball shape would end up as a slightly distorted cube). But if the problem is that the sides have to be pretty much flat, then a dodecahedron would work fine.
I realize the trade off and have settled on a 3 or 4 “gore” shape. I’m just trying to find one that hasn’t been distorted to preserve continental integrity on maps.
This is pretty ugly. but what you are probably looking for is a flattened approximation of a spherical patch defined by a tetrahedral projection onto a sphere. Buckminster Fuller invented the geodesic dome which is an approximation of a sphere using triangles. Fuller generally used an icosahedral (20 sided) projection, but any regular polyhedron could be used. This site gives the chord lengths of a 5 frequency patch (5 chords along each side). This is of course, a 3 dimensional object and would have to be flattened. An easier solution might be to just use 20 regular triangles in order to approximate an icosahedron.
An icosahedron is a pretty good approximation of a sphere and would make the best use out of whatever material you are making the covering out of. Look at the “net” picture in the link and you can picture how easy it would be to contruct a large swath of triangles and cut a bunch of zig-zag lines to get however many covers you need.
Ok, take a look back at my original link, specifically at the “Interrupted Mollweide map, simplified lobes.” See how simple that is? That’s what I’m looking for but I think that shape is morphed to fit the land masses which is something I don’t need. Here is the link again:
