There are an infinite number of roof designs, but the CalFire Draft Guidelines reference four.
Here’s what’s called a gable roof:
A gable roof has a single ridge line, and two roof planes, one on either side of the ridge.
Here’s a cross-gable — two gables intersecting each other:
Here’s a hip-roof:
There’s still a single ridge line, but now four roof planes. Note that none are rectangular. That’s important, because panels are rectangles, and hip roofs aren’t. So lots of space becomes unusable.
The fourth type of roof addressed in the draft is cross-hipped — two hip roofs intersecting each other:
Once again, no rectangular roof planes.
In the real world, roofs can be extremely complicated:
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