The same three basic rafter cuts are used on common, jack, valley, and hip rafters.
Bevel cuts also known as side or cheek cuts are used on the top of valley or hip rafters where they meet a ridge board.
On top of hip jacks where they meet the hip.
On the bottom of valley jacks where they tie into the valley.
The only cuts used on a common rafter are the plumb and level.
Hip and valley rafters are laid out and cut in the same manner. They both have a single or double beveled plumb cut where they meet the ridge board and a bird's mouth where they sit on the inside or outside wall corners.
Hip jack rafters have a bird's mouth, tail, and beveled plumb cut where they meet the hip rafter.
Valley jack rafters have a square top plumb cut for the ridge board and a bottom beveled plumb cut for where they meet the valley rafter.
Cripple jack rafters have a top and bottom beveled plumb cut for where they meet the hip and valley rafters.
Also called a mystery hip (its a mystery where it goes) have cheek plumb cuts on both ends.
Flying hips run from an upper ridge to a lower ridge and tie in uphill of where a valley meets the lower ridge board.