# Making a sphere from a 2 dimensional surface. **URL:** \ **Category:** Factual Questions\ **Created:** [March 5, 2007, 5:34am UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643 "2007-03-05T05:34:14Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![KidCharlemagne](https://avatars.discourse-cdn.com/v4/letter/k/ed8c4c/32.png) [@KidCharlemagne](https://boards.straightdope.com/u/KidCharlemagne)\ **Post date:** [March 5, 2007, 5:34am UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/1 "2007-03-05T05:34:14Z")
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: [http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html#IGoode](http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html#IGoode) 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? ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [March 5, 2007, 6:49am UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/2 "2007-03-05T06:49:25Z")
Have you ever seen a tennis ball? That’s a two-gore shape FTW. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 5, 2007, 7:12am UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/3 "2007-03-05T07:12:35Z")
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? ---
**Author:** ![iPost](https://avatars.discourse-cdn.com/v4/letter/i/858c86/32.png) [@iPost](https://boards.straightdope.com/u/iPost)\ **Post date:** [March 5, 2007, 1:17pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/4 "2007-03-05T13:17:03Z")
I used this shape when I made a hacky-sack out of an old T-shirt. It sucked pellet filled balls! [![](https://www.porkbelly.net/azupload/uploads/smam/sphere.jpg) ](https://www.porkbelly.net/azupload/uploads/smam/sphere.jpg) ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [March 5, 2007, 1:41pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/5 "2007-03-05T13:41:13Z")
How about using an unfolded Dodecahedron, or even an Icosahedron. Or the “clipped dodecahedron” shape of a soccer ball or Buckyball? ---
**Author:** ![KidCharlemagne](https://avatars.discourse-cdn.com/v4/letter/k/ed8c4c/32.png) [@KidCharlemagne](https://boards.straightdope.com/u/KidCharlemagne)\ **Post date:** [March 5, 2007, 2:04pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/6 "2007-03-05T14:04:30Z")
[QUOTE=MrDibble] Have you ever seen a tennis ball? That’s a two-gore shape FTW. [/QUOTE] 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. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [March 5, 2007, 2:14pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/7 "2007-03-05T14:14:51Z")
[QUOTE=CalMeacham] How about using an unfolded Dodecahedron, or even an Icosahedron. Or the “clipped dodecahedron” shape of a soccer ball or Buckyball? [/QUOTE] 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. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [March 5, 2007, 2:20pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/8 "2007-03-05T14:20:19Z")
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. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [March 5, 2007, 2:22pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/9 "2007-03-05T14:22:02Z")
[QUOTE=Mathochist] 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. [/QUOTE] I’m not a betting man, but if I were, you’d be on and my money would be on [this](http://www.vendian.org/mncharity/dir3/planet_globes/TemporaryURL/earth0_globe0.jpg) twelve-gore shape. ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [March 5, 2007, 2:50pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/10 "2007-03-05T14:50:46Z")
You seem to be wanting a very simple shape; but you have to face the fact that the more “complicated” the shape, the better the fit. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [March 5, 2007, 3:06pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/11 "2007-03-05T15:06:11Z")
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. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [March 5, 2007, 3:08pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/12 "2007-03-05T15:08:45Z")
> [@](#): > > 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. 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. ---
**Author:** ![KidCharlemagne](https://avatars.discourse-cdn.com/v4/letter/k/ed8c4c/32.png) [@KidCharlemagne](https://boards.straightdope.com/u/KidCharlemagne)\ **Post date:** [March 5, 2007, 3:55pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/13 "2007-03-05T15:55:01Z")
[QUOTE=panache45] You seem to be wanting a very simple shape; but you have to face the fact that the more “complicated” the shape, the better the fit. [/QUOTE] 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. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [March 5, 2007, 5:38pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/14 "2007-03-05T17:38:19Z")
[QUOTE=Mathochist] 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. [/QUOTE] Naah, I was wrong, although I can see making a single piece out of the tennisball shapes by joining them. Kind of a t-shape, I think. ---
**Author:** ![Darryl\_Lict](https://avatars.discourse-cdn.com/v4/letter/d/7cd45c/32.png) [@Darryl\_Lict](https://boards.straightdope.com/u/Darryl_Lict)\ **Post date:** [March 5, 2007, 10:48pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/15 "2007-03-05T22:48:48Z")
Wouldn’t a “bloated” tetrahedron work? 4 triangular faces each with symmetrical convex sides. Maybe I’ll try to google it up for an exact description. ---
**Author:** ![Fear\_Itself](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fear_itself/32/19637_2.png) [@Fear\_Itself](https://boards.straightdope.com/u/Fear_Itself)\ **Post date:** [March 5, 2007, 11:13pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/16 "2007-03-05T23:13:40Z")
[QUOTE=panache45] You seem to be wanting a very simple shape; but you have to face the fact that the more “complicated” the shape, the better the fit. [/QUOTE] In that case, a [32 face truncated icosahedron](http://www.allaboutall.info/images/thumb/2/28/300px-Truncated_icosahedron_flat.png) would be an even better fit. ---
**Author:** ![Fear\_Itself](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/fear_itself/32/19637_2.png) [@Fear\_Itself](https://boards.straightdope.com/u/Fear_Itself)\ **Post date:** [March 5, 2007, 11:24pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/17 "2007-03-05T23:24:09Z")
Or how about Buckminster Fuller’s [Dymaxion Map](http://en.wikipedia.org/wiki/Dymaxion_map)? ---
**Author:** ![Darryl\_Lict](https://avatars.discourse-cdn.com/v4/letter/d/7cd45c/32.png) [@Darryl\_Lict](https://boards.straightdope.com/u/Darryl_Lict)\ **Post date:** [March 5, 2007, 11:29pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/18 "2007-03-05T23:29:54Z")
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](http://www.tekcad.com/monkeyhouse/geodesics/tetra/) 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. ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [March 5, 2007, 11:35pm UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/19 "2007-03-05T23:35:19Z")
An [icosahedron](http://en.wikipedia.org/wiki/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. ---
**Author:** ![KidCharlemagne](https://avatars.discourse-cdn.com/v4/letter/k/ed8c4c/32.png) [@KidCharlemagne](https://boards.straightdope.com/u/KidCharlemagne)\ **Post date:** [March 6, 2007, 3:59am UTC](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643/20 "2007-03-06T03:59:33Z")
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: [http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html#IGoode](http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html#IGoode) [Next page](https://boards.straightdope.com/t/making-a-sphere-from-a-2-dimensional-surface/394643.md?page=2)