These Plants evolved in an environment of extreme competition for sunlight, and growing a completely opaque canopy became their "weapon" of choice. They would grow a perfectly flat, umbrella-like crowns and block all the sunlight, killing the competition underneath.
At first, these plants had normal drop shaped leaves, but those would capture sunlight imperfectly. Over time, their leaves grew more lozenge shaped, so they could mesh better with one another. From there some sub species speciated to have square leaves, while some grew perfectly triangular ones. A few rarer species evolved perfectly hexagonal leaves.
Time passed, and these leaves became so perfectly shaped (perfect angles, straight lines etc) that when their edges touched they would not only block nearly all sunlight, but capture most water too, and funnel it towards their own trunk. The space between the leaf edges was just too narrow for water to seep through, and acted like a capillary grid instead.
This presented one problem though: a perfect grid of leaves made it impossible for the plant's own flowers to bloom through, without disrupting the grid. It caused the plants to grow flowers with petal shapes complementary to the leaves: for example, the Square-leaf Tree evolved flowers with right-triangle petals, that would perfectly fit in into a square grid once opened.
"Shape wars". Of course, since plants compete, this presented a problem for them. When a Triangle-leaf and Square-Leaf plant grow side by side, their crowns would disrupt each other's grids, since a perfect triangle and a perfect square cannot align. This intense competition would cause both to evolve new weapons: like square leaves that are exactly 1/2 of the regular square leaf, but can be inserted into a triangular leaf configuration to disrupt it, or a very long and narrow triangular leaf that can "cut into" a square grid.
Some plants even managed to grow a form of symbiotism out of it. For example the Square Inch Leaf plant and the Two-inch Rectangle Leaf plant mesh with each other perfectly and share water.
On swamps and ponds, there are entire symbiotic colonies of Hexagon floaters that mesh perfectly together, and can even rotate and reconfigure to defeat their non-hexagonal "enemies".
Some of the hardiest trees take it a step further. They evolved to fold their leaves into cubes made of 8 leaves each. The cubes would then harden into a dense, perfectly cubic nutshell with a seed inside. This "seed box" would be extremely durable, because it evolved to sit and wait on the forest floor for decades, if not centuries, until some breach in the canopy would allow sunlight and water in, thus allowing it to sprout.
This means that the dead, dark, dry forest floor would be littered with billions of wooden boxes (some no bigger than a matchbox, some the size of a shipping crate!) The strange fungi and lichens of the forest floor would thus evolve into angular sheets that could grow between and around these cubes. Animals, in turn, would evolve to utilize the cubical wooden spaces, turning into "Jack-in -The-Box" like creatures, crawling rectangular sheets, or even living forlifts.
In effect, you have a whole ecosystem of enforced straight lines and angles, where squares and cubes reign supreme, and triangles aggressively try to fill niches.
