Gridding depends on the terrain and how much gridding you can do. There are a variety of possible hex formations. The triangle is just the most basic one. It depends on what you have in addition for adjacency, whether you can afford to buy the tiles for it, and whether the District benefits from adjacency at all. Obviously, you want to reserve the central spots for those that benefit most from adjacency, and if the tip of one of the triangles is just Desert, well then that's a good place for an Encampment or Entertainment District.
Three cities throwing their districts together, and then building your empire in three-city regions is one of the approaches to Civ 6. Another one is to build the entire empire on a gigantic hexagonal grid, with each city more or less seeing to its own adjacencies. The two approaches are mutually exclusive. If you have a bunch of cities throwing their Industrial Zones into the center, then none of those Zones will participate in the production of a new city.
If you build in a giant grid, You don't pay as much attention to District adjacency. Instead, you exploit terrain adjacencies and then each city throws production to the center and to the two adjacent cities. There's a central city and six orbital cities. The six orbitals mainly throw to three cities - the center and each adjacent one. So each orbital city gets three Factory bonuses - one for each neighbor and the central city. The central city gets 7 factory bonuses - one for each orbital and its own. Of course, you build the Colosseum and the first Entertainment Complex in Rome. Wait, did I say Rome? I meant Central City. All roads lead to your capital, whatever Civ you build, of course. Having a central Colosseum means you throw the benefit to 7 cities.
The Capital itself will tend not to favor Industrial first, if it's not in a good spot. After all, once the orbital get their factories up, it'll get a lot of help building a central IZ in no time. Alternatively, if the capital is Production-rich, then it can get its Factory up first and help a lot of the peripheral cities along.
Both strategies could be in play at the same time, since getting a perfect hexagonal grid is often not achievable on a Standard map. Deserts tend to get in the way. Water, too. So if you only have 4 points of the hexagon up, you can pull back the factory center towards the end that's populated. That will allow those respective cities to participate in a local three-city regional setup just outside the civ-wide hexagonal interaction.
Of course, each hexagonal orbital city can help to set up a new city along its locality, and once it's set up, they will have a two-city interaction. The orbital will then have 4 cities feeding it, which can end up competing with the capital for productive capacity!
In settling a new site (in another continent, or in a dedicated three-region style), it's often best to set up two or three cities at once past Industrial, just to get them up and running faster. You'll want two cities already founded once the new Factory comes online.
