# What circumstances could lead to city layout based on hexagons?

Most modern planned cities are based on grid layouts. Historic cities are more organic on a macroscopic level, but buildings are still generally square-shaped leading to grid-based layouts on the micro-level.

But I recently learned that squares are boring and Hexagons are the Bestagons due to their many interesting tiling properties. So building a city based on a hexagonal tiling instead of square tiling could be an interesting divergence from how cities are usually planned.

Roads would go in 3 possible angles instead of 2, going across the edges of the hexagons. So the size of the basic hexagonal tile of the city would be size so that the edge length would be the width of a road.

The basic shapes of buildings would also be based on 60° angles instead of 90° angles. Buildings would be hexagonal, triangular (covering 3 hexagons, or for very small structures a 6th of a hexagon) or parallelograms (covering 4 hexagons). Even larger buildings would be extensions or combinations of these shapes:

But the question is: Why would anyone do that? Lots of societies on Earth figured out how to build houses. And they all independently came to the consensus that rectangular buildings are the preferred shape, which in turn lead to city layouts all around the world dominated by rectangles. So what circumstances could lead to a society planning their buildings and thus their cities based on hexagons instead?

I am open to both answers based on historic reasons as well as objective reasons for building future cities that way.

• Comments are not for extended discussion; this conversation has been moved to chat. – L.Dutch - Reinstate Monica Nov 12 '20 at 3:52
• Perhaps buildings tend to be rectangular because rectangles can be perfectly tiled into rectangles, but hexagons cannot be perfectly tiled into hexagons. You can see in your picture that there is some unused space. – Pablo H Nov 12 '20 at 21:09
• Maybe because it's the largest library ever made? – rafa11111 Nov 13 '20 at 1:42
• @PabloH Tesselation is the word you're looking for. – DKNguyen Nov 13 '20 at 2:20
• Hexagons are the bestagons. – Nuclear03020704 Nov 13 '20 at 14:19

### Optimal public transport accessibility for a zero-car city.

A city designed from the ground up should be designed so that cars are unneeded:

• 90% of your reasons to leave the home are serviced within a short walk and no public transport.
• Travel from any point in the city to any other should require no more than a short walk to a public transport point and a short walk from one.

While designing this city, a guiding principle could be "No-one should live more than 5 minutes walk from a subway station!" - this results in a city design where circles 5 minutes walk (ie 500 meters) around a transport centre are tightly packed as much as possible. Eg we get a map of a single suburb like this:

Following the doctrine of Circle Packing we get a hexagonal grid

In that city design 90.7% of the city is 5 minutes walk from one of those hubs. The other 9.3% could be things that don't feature in peoples commutes - solar farms, wind turbines, water storage, etc. Or perhaps it could be parks.

Were this design to be based on squares instead of hexagons, only 78% ($$\pi\over4$$) of the city would be within 5 minutes of a subway station, and getting it up to 90% would create more hubs, adding costs.

### Or - Domes are needed - the atmosphere is poisonous

Eg this Mars colony uses a hex grid layout (for the same circle packing reason):

2 different people commented: "intersections will be harder cause cars will have to check more directions" - no they won't. There are zero cars in this city. You walk a few hundred meters to everything you typically need, and everything else is a subway trip. Retailers are at the hubs so can use freight networks directly. Foot paths out into the suburb can take the odd forklift delivering white goods or construction materials the few hundred meters from hub to home if needed.

### More about the suburb design:

Each suburb is about 780,000 square meters

Your hub in the middle has everything most people need. Shops, post office, doctors, childcare, playgrounds, dentist, physio, pharmacist, restaurants, cafes, vet, a church or 2, and a small school (only a few year levels - not all, some students will need to travel for school). Few medical specialists (but not a full set - may need to travel for specialist medical) A police station (10 cops), fire brigade (3 vehicles), and 5-bed emergency department also feature in the hub. The whole hub complex is taking up about 180,000 square meters of space in the middle.

The inner ring around this is offices and dense living. 3 or 4 story buildings, 1-3 bedroom apartments. Maybe 200,000 square meters or so.

The outer ring is low density living. 3 bedroom houses on 400 square meter lots sorta thing. There's about 800 low density homes around the edge of the suburb.

Your looking about 10,000 people in total, 3000 commuting in peak hour. Well within the capabilities of modern subway systems. Freight is unloaded in side stations to avoid stalling the main lines.

Foot paths out to suburbs are wide enough for a vehicle to travel on, and are used by emergency services, as well as the occasional forklift delivering construction materials or really big eBay order.

Basic services are duplicated (eg 1 grocery store in each hub), but specialists require a commute, eg only one suburb in 4 has a Catholic church, one suburb in 5 has a pet store, only 1 in 50 has a brain surgery operating suite.

• Notably, the Paris Metro is designed so that any point is within 400m of a station, though the streets aren’t regular. – StephenS Nov 11 '20 at 14:27
• Definitely not trying to design a scalable railway line design for such a city. Nosir. Not me.. More seriously: Throw a centrally scheduled Private Rail Transit system at this design and you get a seriously utopian vision of inner-city transport. – Joe Bloggs Nov 12 '20 at 7:33
• @JoeBloggs On it's pretty complex. I had planned this out as this is borrowing into some fiction I had started. You have "local routes" doing hexagon loops of 6 adjacent stations, and then "express" lines doing larger and larger hexagons. There was no transfers - I'm planning on actually having the subway cars of a moving train detach, switch onto other lines, and recouple with new trains. You use an app to guide you "At 8:27am board the train at platform 2 in car 4. After 3 stops, transfer to first car. Wait 4 stops. Transfer to second rear car. Alight at 3rd stop." – Ash Nov 12 '20 at 8:31
• See also 15-minute cities - every basic amenity (including vital nature) is a short walk or bike ride away. – thosphor Nov 12 '20 at 10:03
• @Ash If you've got an App and individual car switching I'd genuinely recommend looking into PRT networks and ride sharing algorithms. Basically treat each carriage as a requestable resource that makes stops based on demand and shared journey optimisation, then just store the carriages when there's no demand. People tap on the app for a pickup at station X in 5 minutes, then go to the station and wait a few seconds: Carriage turns up and off they go. All routing/scheduling can then be handled efficiently by computer. – Joe Bloggs Nov 12 '20 at 10:16

The city was planned, it did not grow, and its founders regarded hexagons as the mathematically superior form.

Perhaps, historically, the hexagon was associated with the chief religion. This may or may not be in current effect; what chiefly matters is that it was in effect when the roads were laid out and the buildings went up, and resistance to having your building knocked down keeps it going.

Perhaps they regarded it as Scientific and Superior and Shaking Off The Dead Hand of the Past. They might cite honeybees as the example of what they want, including that it maximizes connectivity with minimum amount of road. (Bees' cells use the least wax for the most space for honey.) Or cite it as the largest number of sides that tessellate, in an era that is much taken with mathematics.

• This is probably the most likely, a lot of bad design gets incorporated into civil structures due to public opinion, religion, tradition, or just plain personal preference of the designer. – John Nov 10 '20 at 14:25
• In Orson Scott Card's Tales of Alvin Makers, hexes are literally made with hexagons; a tattooed hexagon can defend the bearer against attacks and the evil eye. "Hex" designs are often incorporated on barns ( eu.sctimes.com/story/life/2018/01/20/hex-signs-barn-quilts/… ). So, it stands to reason that a planned city might be hexagon-based because people feel safer - and once the tradition started, it would be well-nigh impossible to build a city in any other way. – LSerni Nov 10 '20 at 15:03
• @Lserni And in a fantasy setting, it might actually be safer! – Cadence Nov 10 '20 at 16:57
• @pipe Interesting bee trivia, they don't make their honeycombs into hex-grids deliberately. The cells are actually made initially as circles, but the wax naturally tends to form into hex-grids and the bees don't care enough to change that. AFAIK, scientists are still studying this and aren't sure what exactly is causing the formation of hex-grids. – Ruadhan Nov 11 '20 at 10:27
• @Ruadhan Nah, it's a rather simple piece of math, and a simple experiment. Stack thin rolls made out of wax into a box, in a way so that always only two rolls touch, never three around a thin channel, and heat them to 40°C overnight. Hexagonal is the only stable structure that can develop, and the bees have no chance to hold the wax in any other form, because it flows. – Karl Nov 11 '20 at 17:41

Hexagonal urban planning is not common but it has already been done:

La Sentiu is a planned neighbourhood near Barcelona with roads in hexagonal directions. Blocks aren't exactly hexagonal but walking though the neighbourhood feels like they were. Maps can be found at http://www.icc.cat/vissir3/index.html?xMUrfgUVS or https://www.google.com/maps/@41.3002961,1.9710314,17z

It was intended to be an high standing suburban neighbourhood, so some reasons for this street pattern can be more or less guessed:

• Aesthetic reasons: There is a trend in urban planning that favours irregularity as a way to get some picturesque results. The most famous precursor of this trend was Camillo Sitte more than 100 years ago. Hexagonal roads avoid the impersonal long straight streets of modern cities while still allowing for some regularity.
• Pacification of transit: Hexagonal roads allow car access to every place but they don't favour speeding because of frequent crosses. The same effect is often pursued by using a lot of roundabouts. An hexagonal grid uses less space and is less annoying for the same goal.
• At the same time, 120 degree corners are safer and less annoying for cars than 90 degree corners. Furthermore, 120 degree corners don't need chamfers to improve visibility, so more space is saved. Judging by the time the neighbourhood was built, I guess than promoting cars was more a goal than pacificating traffic.
• Additionally, intersections in hexagonal grids are 3 way intersections, instead of the common 4 way intersections found in square grids. That makes them very easier to navigate for motorists.
• By the time it was build, hexagons and other geometrical follies were modern looking. Just to cite a contemporary example, the Ethnology Museum in Barcelona plan is also based on an hexagonal grid.
• And as other answers have correctly pointed, the ratio between street area and usable land area is slightly better for an hexagonal grid than for a square grid.

And that has been just a quite anecdotal summary based on a single real case. An essay long summary on the state of the art of hexagonal urban planning can be found at http://web.mit.edu/ebj/www/Hexagonal.pdf .

• When you said "120 degree corners are safer", did you mean 60 degree corners? – Emilio M Bumachar Nov 12 '20 at 18:09
• @EmilioMBumachar - I meant 120 degree. I'm measuring the interior angle in the hexagonal city blocks. Maybe you are measuring the exterior angle in the same geometry, or maybe you have triangular (not hexagonal) city blocks in mind. Anyway, I meant the kind of corners shown in the photograph and the map. – Pere Nov 12 '20 at 18:40

## Unstable Land Surface

Imagine that the ground itself expands and contracts slowly over time. This could be due to frost heave on an enormous scale, or the absorption and release of water over time. To completely pave over such a location would be fruitless - the stress from the expansion of the ground underneath would turn the pavement to rubble. Gaps have to be left to allow for the expansion, and the most efficient way to do that is to create a hexagonal grid.

The phenomenon is extremely common on a small scale. Soils with significant amounts of certain clays (e.g. smectite, vermiculite) shrink and swell substantially when they lose and gain water. Here's a parched example:

Of course, these aren't perfect hexagons, but even at this small scale the tendency towards 120-degree angles is apparent. This is not a coincidence - when a membrane "blisters", it will naturally tend to do so by breaking into three identical parts meeting at 120-degree angles. The larger the scale, the more the mathematics matters and the more perfect the angles.

Thus you have a choice. Either your city was engineered in hexagons, as this is the most efficient way to provide room for expansion. Or it was forced into (perhaps imperfect) hexagons by the natural breaking up of the expanding landscape. And perhaps both are true.

I think its fair to say people tend to do things long after the original rationale has ceased to exist (e.g. people in the UK drive on the left-hand side of the road because knights on horseback preferred to have each other's sword hands in view). So for me it's more plausible that the hexagonal form predated any advanced technology (as opposed to suggesting that advanced technology dictated a hexagonal form).

Perhaps the local tree-like fauna always sprouts branches at a 30 degree angle from the main trunk, and it was easier to incorporate the branch/trunk joints into early wattle-and-daub style huts than it was to hack the branches off the trunks with stone tools, so the first huts were hexagonal. Hexagonal became established as the traditional shape and everything else flowed from that.

I've seen a hexagon-based city in a sci-fi story and I believe the reasoning was sound:

The city was on the ocean, not on land. The "land" of the city was a collection of hexagonal platforms--basically huge hexagonal concrete cups that were inverted. They float because of the air trapped underneath. The concrete extends deep enough into the water that even the most extreme waves will not let the trapped air escape. So long as they are wide enough compared to their depth they're stable.

Roads were not an issue because they couldn't exist anyway--each city block floated independently from the ones around and there would be some flexing at junctions. IIRC transport was by boat.

• that is not really a city, more of a village, people need to move around a city. – John Nov 10 '20 at 23:15
• @John They did--by boat. – Loren Pechtel Nov 11 '20 at 4:07
• Venice of the hexagons. – pjc50 Nov 11 '20 at 8:55
• But why hexagons specifically? Why not some other shape? – MJ713 Nov 12 '20 at 18:07
• @MJ713 The only three options are triangles, squares and hexagons as they are the only shapes that tile without gaps. For a given structural strength I think hexagons will permit the biggest tiles. – Loren Pechtel Nov 13 '20 at 3:10

It's a city of bees

Who says that the species of the denizens has to be human?

If bees evolved to where they began to make cities, they might just use the hexagon shape, because that's what seems natural to them.

## Because Your City has Celtic Origins

Many answers have already brought up how circles can force a hex pattern, or how much tradition can influence things, but this combines both of these ideas into one. Unlike most civilizations, Celtic homes were built in circles, not squares. Instead of having their hearths off to the side of the home where it would be out of the way, the Celts built their homes around the hearth in a circle to evenly heat the home.

This often lead to roughly hexagonal path systems between their roundhouses to optimize space. Had Celtic civilization not be supplanted by the Romans and their rectangular architecture, their towns would have eventually built up into full sized hex grid based cities forcing developers to either wipe out everything and start over or to continue the tradition of using hexagonal roads and land plots.

Since wiping things out and starting over again is so costly, your city has maintained the hex layout as part of its proud celtic tradition.

# Because the city is vertical

I love the other answers on this post a lot, but since no one mentioned it, I thought this was a cool idea.

If you want a city embedded in a cliffside to be walkable, one of the easiest ways to do that would be to use – basically – a honeycomb. The diagonals would have stairs on them, the flat sides would be sidewalks. This has a few advantages: first, no one has to climb a ladder (easier to carry things!); second, since it's closer to a circle than a square, it has a better volume-to-perimeter ratio, meaning more room for less wall; and third, it's a solid, strong structure that distributes weight well.

Maybe the hexagonal planning had nothing to do with the surface, but rather some subterranean phenomena, such as extreme seismic activities!

They had to create a huge hexagonal structure under the surface (kind of like a buildings foundation) as resistive measures. Then, the surface structure would naturally reflects how the foundation is shaped. They may even have done it on more than one layer!

Brief summary: solitude / social distancing, lack of external enemies, nomadism.

According to Why are Most Buildings Rectangular (well worth reading), the trend from circular houses to rectangular buildings in human societies has generally coincided with (1) a demand for larger houses to pack larger, wealthier families into a single building; and (2) a need to pack a growing population efficiently into a small space for defense.

With regard to (1), the paper shows why rectangular buildings with rectangular rooms offer better flexibility of design and dimension for packing rooms into a building. If the society you are writing about is a society of hermits who prize solitude, have very few children, and eschew the accumulation of possessions, there would be little demand for interior rooms, and therefore little reason to prefer rectangles. As such, the advantages of hexagonal design (described in other answers) could prevail.

(A hermetic people might prefer not to live in cities at all. And perhaps most of them don't. Why then have such a city? Perhaps the supreme leader has a vision to do something great ... like build a super-awesome statue, or develop a vaccine against the plagues ... that requires a high concentration of scientific, industrial and economic activity.)

Another factor contributing to a preference for solitude could be recurring waves of plagues (like the current pandemic). In such a world, the ability to isolate families from one another quickly could be a life-or-death issue. Large buildings, i.e. buildings used by many people at once, might be seen as a disgusting tendency, like sharing toothbrushes. Again, small buildings need fewer internal rooms, so the flexibility of room packing with rectangles is less compelling.

With regard to (2), without the need to pack many people efficiently into a finite walled area for defense, a pressure toward rectangular buildings is reduced.

Another factor could be that the city is planned as a nomadic one, due to seasonal environmental factors; the buildings are portable, and are moved from Summer City to Winter City and back every year. This is only possible if the buildings are small, without many internal rooms, and therefore they need not be rectangular. Simple, one-room portable buildings are easy to build as structures radiating from a central support pole, of which the hexagon shape is a sweet spot between complexity (many walls) and space (ratio of floor area to perimeter).

In this scenario, the hex-aligned streets of the city (and maybe a few key buildings and infrastructure) would be permanent, with uniform modular hexagonal lots to accommodate the hexagonal houses that come and go. There could be more prestigious lots and more slum-like areas, and the locations of individuals' and clans' houses would change from year to year based on some sort of status or performance.

From the Centuriation of the Romans to Mansard roofs of Paris, city layouts and building design are often heavily influenced by surveying technologies, title law, and tax law.

Perhaps the hex city surveyors employed a surveying method that favors approximately circular divisions: the surveyor's guild has a single Gunter's chain, and the lots thus constructed follow in the same was as construction of hexagons using compass, the regularity following from the single measuring tool used. Alignment was initially based on a mountain or star or other landmark, but once set is now locked in place given the recursive and uniform nature of surveying. Surveys and title are per hex.

Taxes were per section as opposed to say counting the stories or number of windows, so with sections divided into hexagons it was most economical to fill in the hex lots with hexagonal buildings.

• Tudor style houses often have larger 2nd stories than 1st stories because property was taxed based on the square footage of the foundation. If you modify this idea to say taxes are based on the longest line you could draw through a building's floor plan, then a rectangle would mean more taxes than a hex or circle. – Nosajimiki Nov 12 '20 at 21:23
• ... for the same total area within the boundary of the shape, that is. You could also make it a measurement of the perimeter, since this is proportional to diameter and radius, it's effectively the same thing, and seems more intuitive to actually be used. – Nij Nov 13 '20 at 3:20

I love the sentient-bee-people idea, and here’s one for the mammals that might have tried to technologically copy them for a crystal city:

“Among the primary crystal systems, the hexagonal system has the fewest substances assigned to it, including arsenic, calcite, dolomite, quartz, apatite, tourmaline, emerald, ruby, cinnabar, and graphite.“ (Quoted from “Brittanica”)

Quartz in particular catches my attention, because that means piezoelectricity and all the alternate technology that could go with it. Ruby could be used for lasers, graphite for writing and lubricating the gears of heavy metal machinery, the “Emerald City” by Baum we already know of, Arsenic implies steel-quenching and metal production again — as well as a whole Guild of Poison-tolerant people who couldn’t safely leave their environment least they be dangerous to others.