Cross hipped roof
The frame structure of a hip roof is more complicated than of a gable roof. This is because the hip roof has 4 sides instead of 2. The ridge board is centered width wise and lengthwise.
The main components of a hip roof are rafters, hip rafters, end common rafters, jack rafters and ridge boards. Rafters run perpendicular the entire width of the structure. Hip rafters have a 45 degrees angle inclination to both the sides of the roof and common rafters comprise the edges of the 4 faces. Common rafters run from the ridge boards to the overhang. Jack rafters are made to run parallel to the common rafters, the difference being that they become shorter because of the intersection with the hip rafters.
Hip roofs can take many shapes, even T and L shapes. They do require a more complicated framing though. The main points of contact of the roof are between the hip rafters and the ridge. For an accurate framing, you will need to perfectly center the ridges.