Corn is pollinated by wind and stands a better chance of producing nice, full ears of corn the more corn plants you have. It’s best grown in clusters, blocks, or staggered rows (rather than a single straight row) to ensure enough pollen gets around to all the plants.
Squash is pollinated by insects, so growing multiple squash plants in proximity will attract more insect activity once they start blooming. (In a pinch, you can also hand-pollinate squash.)
Beans are self-pollinated and will produce beans even with just one plant, but in an intensively planted garden bed like a Three Sisters, they tend to have a slightly lower yield so you’ll get more beans the more plants you have.
My 4×6 bed in these images sits against a wall, so I sowed the corn across the back first, placing a seed in a staggered row every 8 inches.
Once the corn seedlings grew 4 to 6 inches tall, I sowed the beans about 6 inches in front of them, placing a seed every 3 to 4 inches, and then the squash along the edge of the bed every 2 feet, letting the vines eventually spill over the side.