The Unnecessary Peril of the Fuller Projection

This is the Fuller projection, and using it could get you in trouble:

Throughout my career, I’ve heard a variety of rumors and conflicting opinions about whether or not that statement is really true. People would tell me that you had to pay a fee to use it, or end up facing a lawsuit. Others said that there was no way anyone could own, or punish you for using, the set of equations that makes up a map projection.

This confusion frustrated me. So, over the years, I’ve done a little research in the hopes of getting a definitive picture of the legal issues (if any) that surround the Fuller projection. Here’s the summary of what I’ve concluded: if you don’t pay a license fee before you publish a map that uses the Fuller projection, you may find yourself hearing from the projection’s “owner.” At the same time, I don’t think that the owner (the Buckminster Fuller Institute) has any rights that would actually hold up in court.

Important side note: We’re going to be talking about legal matters here. I am not a lawyer. None of this is legal advice.

Let’s dive into the details.

Quick History

The Dymaxion World

In 1943, inventor/designer/architect R. Buckminster Fuller published the “Dymaxion World” map in an issue of Life magazine. It’s a polyhedral projection; many other such projections exist in this category. The general idea is: project the globe of the Earth onto a 3D shape made of flat sides (a polyhedron).

Fuller, holding a polyhedral globe (from the Life article).

After that, you can unfold that polyhedron in a variety of ways to yield a flat map.

Two different unfoldings of Fuller’s polyhedral globe, again from the magazine.

Fuller received a patent for this particular polyhedral projection in 1946, which expired in 1963.

In the end, though, this is not the projection we’re looking for. Notice that the shapes it’s made from—the faces of the polyhedron—are different than the map that I showed at the start of this post. The “Dymaxion World” is based on a cuboctahedron, made of six squares and eight triangles. The version of the Fuller projection that you will find in ArcGIS (and scant few other places) is instead based on an icosahedron, which is made of twenty triangles.

The first Fuller projection uses a cuboctahedron, whereas the “modern” Fuller uses an icosahedron (and then further slices up a couple of those triangles).

Even though it’s not what we’re looking for, this earlier projection (let’s call it Fuller I) is worth mentioning because it’s often talked about interchangeably with the more commonly seen version of the projection (the one we actually want).

The Airocean

By 1954, Fuller had teamed up with Shoji Sadao to produce a map using a different polyhedral projection. This map, the “Dymaxion Airocean World,” uses an icosahedron, yielding the form of the Fuller projection that most of us are familiar with.

Now, the method for projecting the globe onto the polyhedron may have been the same, but the particular polyhedron it was projected onto is different, so to my mind this is a different projection. Fuller seems to disagree, though, because in the bottom right corner of the map, you find the following:

Fuller refers directly back to his 1946 patent, so in his mind, the projections are the same. He also claims copyright over the map itself. We’ll get back to both of these things later. Meanwhile, though, this is the actual projection we’re looking for, in the earliest published form that I can find. The 1953 map that he refers to is on the Fuller I projection.

Let’s call this icosahedral version of the projection the Fuller II, for clarity.

The Buckminster Fuller Institute

Fuller died in 1983, and his intellectual property is now held by the Buckminster Fuller Institute (BFI). That would include any copyrights, trademarks, or other protections that may or may not apply either to his map projections or the specific maps he made. As such, BFI claims ownership of the Fuller projection(s) and requests the payment of a fee by anyone who intends to make a map in that projection. Later on we’ll discuss why I think they have no right to do so, but let’s review what they say.

BFI’s Claims

Their website has since been updated, but at the beginning of this year, it had a page that stated: “The word Dymaxion, Spaceship Earth and the Fuller Projection Map are trademarks of the Buckminster Fuller Institute. All rights reserved. Please send inquiries regarding use and licensing the Fuller Projection to”

And, on another page that has also since been removed, they inform us that “BFI is the agent of the Estate of Buckminster Fuller’s copyright of The Fuller Projection Map. Please contact us for permission to use.”

In an email exchange I had with BFI in January through April of this year, they confirmed their requirement of a license, and pointed me toward Fuller’s original 1946 patent. They also indicated that their license is typically free for a nonprofit use and “a few hundred dollars” for a commercial use.

Others, too, have received a similar response from BFI. For example, in a comment thread discussing potentially implementing the Fuller projection in D3, Curran Kelleher (Github user curran) reports being told by BFI in 2017: “BFI owns the rights to the projection, and yes, it requires a licensing agreement for use.”

So, based on the above, BFI offers three bases for their claimed ownership of the Fuller projection: patent, copyright, and trademark. Now, I will again remind you that I am not a lawyer, but I find all of these to be dubious. Let’s have a look.


The US patent expired in 1963. I am not aware of any extension, or subsequent patent, granted to Fuller for a map projection. If you know of any, I would welcome that information. Even if there are others, Fuller died in 1983, and any patents filed within his lifetime should have expired by this point.

Interestingly, by claiming protection from an expired patent, BFI is following Fuller’s own example. Almost twenty years after the end of his US patent, Fuller published a map in 1982 with a notice that once again invoked its nonexistent protection.

Besides the issue of it being long since expired, it’s not clear that the patent ever protected the Fuller II version of the projection that he began using in the 1950s. Fuller is explicit in the patent that his method involves projecting the globe onto a cuboctahedron. All of his examples in the patent show the Fuller I version. He does not discuss projecting the globe onto any other polyhedra.

Obviously, based on the notices he appended to his maps, Fuller believed that his original patent applied to the Fuller I version. And perhaps a judge could be convinced to construe the patent as applying to projections developed on other polyhedra, such as the Fuller II. But, again, if it ever applied at all, this patent expired decades ago. BFI can find no comfort here.


When you make a map, or write a blog post, or otherwise produce a creative work, you automatically hold copyright to that work. Fuller produced several maps using his projections, and BFI has the exclusive right to print and display those. Taking any of them and selling them yourself would be wrong.

But copyright is for specific works, not for general designs. When Fuller changed the colors or labels on one of his maps, that became a new map with a new copyright. Likewise, if you produce your own map, one that looks sort of like his but is clearly different, then you have not violated copyright. The broad shapes cannot be copyrighted, only the specific details of each individual map. If simply using the same projection as another map was a copyright violation, there would be very few maps indeed.

BFI is correct in guarding their rights to the specific maps that Fuller made. But when they say, “BFI is the agent of the Estate of Buckminster Fuller’s copyright of The Fuller Projection Map,” it appears they are trying to claim copyright over anything that uses the projection (since “The Fuller Projection Map” doesn’t really refer to any specific map). This is not just how it reads to me: as we’ll see below, they have previously threatened legal action on that exact basis.

And, again, Fuller made two different-looking projections, so it’s not even clear which one they’re claiming.


BFI’s use here is a little unclear. Their webpage used to say, “… and the Fuller Projection Map are trademarks of the Buckminster Fuller Institute.” Does this mean the phrase “Fuller Projection Map” is the trademark? Or perhaps they mean to claim that the map drawing itself is trademarked, which is not really possible. Phrases, wordmarks, and small iconic graphics can be trademarked. The mathematical transformations of a map projection cannot be. Patents are for protecting the projection method, and copyrights can protect the individual maps that come from the method. While it’s true that you can trademark a specific graphic mark, an entire map is very different than a small brand-identifying logo.

On the other hand, BFI does have a right to control the use of the word Dymaxion. That’s a word that Fuller frequently applied to his inventions, including his projections. If I used that word on my map, I might mislead people by implying that I’m endorsed by, or connected to, Fuller or BFI. Thus, it’s best to refer to the Fuller projection, rather than the Dymaxion projection.

Trademarks are for words and logos that define your brand, and only offer protection in limited contexts for distinguishing your organization from others. They do not apply everywhere, to every map that has the same shape regardless of its size or content. For what it’s worth, I was not able to locate a registered trademark that matched BFI’s claim, though that may well be down to a lack of search skill on my part.

An Easing?

As I mentioned, I reached out to BFI earlier this year, asking them to be more specific about their claims: could they point me to the legal basis they had for insisting on a license fee? Unfortunately, they could not. I was told that, due to time constraints on their small staff: “I’m afraid providing you with the definitive answer is out of reach … unless we at BFI invest several hours of time and consult with our attorneys.”

However, around this same time, it appears BFI reorganized their website. While in their emails to me they still spoke of a license fee, they removed mentions of their ownership of the Fuller projection from their website. Now, they have a general “Licensing” page that only asserts ordinary copyright on specific maps that Fuller made, which is well within their rights.

I’m not sure what’s going on behind the scenes at BFI. I’d like to think that my inquiries prompted them to scale their claims back, but the timing of the website changes leaves some room for doubt. According to the Wayback Machine, the old claims were up through at least January 2022, and the new pages started appearing in March 2022. I emailed them in two bursts: January 2022, and April 2022. Even if their website apparently no longer said so in April, they still spoke to me as though a license was needed.

Thus, I’m not sure if they are planning on still enforcing their nonexistent ownership. They were not really able to offer much in response to my inquiries last time, so I’m hesitant to contact them again to find out. For now, I would not assume they have relinquished their claims.

Damage Done

Even if they no longer intend to assert ownership over the projection, their past actions have likely harmed others, by extracting fees from them to which BFI had no right. It is easy to imagine that others, in lieu of paying those fees, were instead forced to alter their works, or shelve creations entirely.

Some people went ahead and made Fuller projection maps anyway without paying the fee. But BFI actively defended its claimed ownership. I know a specific example of colleagues who were sued by BFI for hundreds of thousands of dollars for producing a map using the Fuller II projection. BFI claimed their copyright had been violated, since my colleagues produced a map that had the same general shape (i.e., projection) as one of Fuller’s from the 1950s. Again, such a claim is baseless—projection is not enough to make two maps similar enough to violate copyright. I’m informed that my colleagues’ lawyer agreed that they had done nothing wrong, but nonetheless advised them to settle and pay BFI (a smaller sum) to avoid the expense of court proceedings.

Whom else did they do this to? Whom else did they threaten into paying fees they had no right to?

It’s important to note that BFI is not a nefarious organization. I don’t know a great deal about them as a whole, but they appear to operate as an educational nonprofit. Any income yielded from their zealous attempts to guard ownership of the projection has, in all probability, been put to good causes. They appear misguided, not ill-intentioned. But a recognition of good intent can only forgive so much.

Their aggressive assertion of ownership, however ill-founded, has had a chilling effect on cartography. Maps have been altered, or not made at all, to avoid the wrath of BFI. Even now, while the Fuller II projection is accessible in ArcGIS, it is not found in a lot of other GIS software, due to wariness of BFI or an inability to pay fees. Interestingly, according to Esri employee Melita Kennedy, BFI asked Esri to include their projection in ArcGIS. Which is interesting, because that feels almost like a trap to me: there it is, appearing in the list of projections that you can use, with little warning that there may be consequences for doing so.


So, to conclude: BFI has, in the past, claimed exclusive ownership over the Fuller projections, and has been willing to enforce that claim with lawsuits. That era may or may not be over, but regardless, any rights expired in 1963 (though, again, it’s not clear the Fuller II projection was even protected by that patent). If I had the financial means, I would invite a legal challenge from BFI to have this settled in court, but short of that, I am left with only theories.

I am not a lawyer, just a production cartographer who’s done some digging. If you know of other salient facts that I’ve left out, please let me know! Meanwhile, I hope this has been useful to you. I presently think you have every legal and moral right to go out and make maps that use either of Fuller’s projections. Nonetheless, there is a risk involved: you can be sued even if you’ve done nothing wrong, and you are likely to be on the hook for legal fees even if you win your case.

9 thoughts on “The Unnecessary Peril of the Fuller Projection

  1. I actually AM a lawyer—one with a deep interest in both intellectual property and cartography—and I believe your assessment is both comprehensive and accurate. A very useful summary!

    Incidentally, the first map I ever drew, for a 8th grade World History assignment in 1971, used this projection. (I’d just read a new biography of Fuller that used it for the endpapers.)

  2. I reached the same conclusions when I researched these claims for D3. However, on top of the patent and the trademark, I noticed a third layer of IP restriction, which is on the actual C implementation of the triangle transformation that Robert Gray wrote for Fuller.

    On Gray’s website (, he has a sentence in which he explicitly opposes any reuse of this code without the author’s permission, a position which might have had merits at some point in time, but is not compatible with free software. To avoid this issue, I made a clean room implementation instead, and distributed it under a public domain license (, which allowed us to release d3.geoAirocean under a free license.

    (More recently I found that a variant of Markley’s projection could result in a beautiful alternative to that projection, which I’ve dubbed the conformal airocean:

    1. Thanks for bringing up Gray. I did think about adding a final note about Gray’s expression of the method, and alternatives like daan Strebe’s “dymaxion-like conformal” ( — maybe I will do a follow-up at some point. My thought is that, even if the underlying math is different, the final map looks similar to a Fuller II projection. And BFI has specifically sued people on the claim that their maps’ projections have a strong visual resemblance to the original Fuller maps. So a person could make a map using any sort of “safe” implementation and still get sued because the outcome looks basically the same. And even if BFI’s claims are ridiculous and can’t hold up in court, whomever they sue will be cowed into paying a fee to avoid the expense of a case.

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