[mjfisher]

Cheaper for everything, ultimately.

A triangle by definition is guaranteed to be co-planer; three vertices must describe a single flat plane. This means every triangle has a single normal vector across it, which is useful for calculating angles to lighting or the camera.

It's also very easy to interpolate points on the surface of a triangle, which is good for texture mapping (and many other things).

It's also easy to work out if a line or volume intersects a triangle or not.

Because they're the simplest possible representation of a surface in 3D, the individual calculations per triangle are small (and more parallelisable as a result).